rism (c48b2)
RISM (Reference Interaction Site Model) module
------------------------------------------------
The RISM module allows the user to calculate the site-site radial
distribution functions g(r) and pair correlation functions c(r)
for a multi-component molecular liquid. These functions can then
be used to determine quantities such as the potential of mean
force or the cavity interaction term between two solute molecules
into a solvent, and the excess chemical potential of solvation of
a solute into a solvent. The change in the solvent g(r) upon
solvation can be determined and this allows for the decomposition
of the excess chemical potential into the energy and entropy of
solvation.
The code was written as an independent program by Benoit Roux
in 1988. Some routines were added and it was adapted for CHARMM
by Georgios Archontis in 1992. The help and advice of Hsiang Ai Yu
is greatfully ackgnowledged.
* Menu
* Syntax | Syntax of the RISM commands
* Commands | Explanation of the commands
* Theory | A brief introduction to the RISM theory
* References | Useful references
* Examples | Input files
Top
Syntax for RISM calculation
---------------------------
Invoke of the RISM command in the main charmm input file
calls the subroutine RISM() (in rism.src). Once control has
been transferred to this subroutine the subsequent commands
are interpreted using a parser similar to the CHARMM
parser.
Main command :
RISM [NSTV int] [NSTU int] [NSOL int]
Enters the RISM module.
NSTV is the keyword to indicate the maximum number of atoms in the
solvent molecule (the default is 6 as defined in
source/fcm/rism.fcm), must be less than or equal to the default.
NSTU is for the maximum number of atoms in the solute molecule(s)
(default is 20), must be less than or equal to the default.
NSOL is for the maximum number of solutes (default is 2), the
allowed values are 1 or 2.
STOP
leaves the RISM module
Subcommands:
1) Miscellaneous commands
( compare with *note » miscom Syntax ).
GOTO
----
LABEl labelname
----
OPEN { READ { NAME filename UNIT integer } }
---- { WRITE { NAME filename UNIT integer } }
STREam [filename]
----- [ UNIT integer]
RETUrn
------
CLOSe [ UNIT integer ]
-----
SET { parameter string }
---
DECR { parameter } { BY value }
----
INCR {parameter } { BY value }
----
FORMat { format-description ((f12.5) or (e12.5) default) }
IF { parameter } { EQ } { string } ... command
-- { NE }
IF { parameter } { GT } { value } ... command
-- { GE }
{ LT }
{ LE }
2) Specific RISM commands
-------------------------
READ { PARAmeters } [show] [UNIT integer (5)]
----
{ STRUcture }
{ COORdinates {( SOLVENT )} }
{ { SOLUTE { integer (1) } } }
{ 2COOr { SOLUTE { integer (1) } } }
{ ZMATrix {(SOLVENT ) }
{ {SOLUTE { integer (1) } } }
{ 2ZMAtrix { SOLUTE { integer (1) } } }
{ CS(R) { ( VV ) }
{ [ UV [ SOLUTE integer (1) ] }
{ US(R) }
{ G(R) }
{ CH(K) [ ( VV ) ] }
{ DC(R) [ SOLUTE integer (1) ] }
{ DG(R) }
WRITe { TITLe }[ UNIT integer (6)]
-----
{ COORdinates ( SOLVENT ) }
{ { SOLUTE { (1) integer } } }
{ CS(R) { ( VV ) }
{ [ UV [ SOLUTE (1) integer ] }
{ US(R) }
{ G(R) }
{ CH(K) [ ( VV ) ] }
{ DC(R) [ SOLUTE (1) integer ] }
{ DG(R) } -
[ PLT2 ] [FROM real THRU real] [FORMAT format-spec]
{ R(I) }
{ RK(I) }
SETUp [ ( LOGFFT ) ] [ NPOINT (512) ] [ DR (0.02) ] [ RMIN (-5.12) ]
----- [ FFT ]
EDTZm [ ( SOLVENT ) ]
----- [ SOLUTE integer (1) ]
STATe [ TEMP real (300.0) ]
-----
[ DENSITY { segment-name-1 real (0.0)
... segment-name-n real (0.0) } ]
[ CDIE real (0.0) ]
ITERate { VV } \
----- { UV } only one of these options
{ UU } / -------------------------
/ [ (HNC) ]
[ PY ]
only one of these options
------------------------- [ PY2 ]
\ [ XTR { AXTR real (1.0)
RXTR1 real (0.0)
RXTR2 real (0.0)
AXTR(2) real (AXTR(1))
RXTR1(2) real (RXTR1(1))
RXTR2(2) real (RXTR2(1))
... } ]
[ INIT ] [ NCYCLE integer (1) ]
[ IUNSCR integer (0) ] [ IUNGR integer (0) ]
[ NPRINT integer (NCYCLE) ]
[ RMIX real (0.33) ] [ NDMAX integer (25) ]
[ TOL real (0.01) [ CDIE2 real (CDIE) ]
[ US(R) ]
[ G(R) ]
[ W(R) ] \
[ TS(R) ]
only one of these options
[ CAV(R)]
[ BD(R) ] /
[ SW(1) real (1.0) ]
[ SWI(1) real (SW(1)) SWF(1) real (SW(1)) DSW(1) real (0.0) ]
[ SW(2) real (1.0)]
[ SWI(2) real (SW(2)) SWF(2) real (SW(2)) DSW(2) real (0.0) ]
[ SW(3) real (1.0)] [ SWI(3) real (SW(3)) ]
[ SWI(3) real (SW(3)) SWF(3) real (SW(3)) DSW(3) real (0.0) ]
[ SW(4) real (1.0) ] [ SWI(4) real (SW(4)) ]
[ SWI(4) real (SW(4)) SWF(4) real (SW(4)) DSW(4) real (0.0) ]
DERIvative [ INIT ] [ SOLU integer (1) ]
----- [NCYCLE integer (1) ] [ NPRINT integer (NCYCLE) ]
[ RMIX real (0.33) ] [ TOL real (0.01) ]
[ CLOS (HNC) ] \
[ PY ] only one of these options
[ PY2 ] /
SOLVation { HNC } [ CHMPOT ] [ ENER ] [ CAVIT ] [ FLUC ]
-----
[ SW(1) ] [ SW(2) ] [ SW(3) ] [ SW(4) ]
[ SOLUte integer (1) ]
[ VERBO ]
[ PLT2 [ FROM real (RMIN) THRU real (RMAX) ] ]
[ UNIT integer (6) ]
ANALysis [ (VV) ]
----- [ UV ]
[ PAIR integer (all pairs) ] [ UNIT integer (6) ]
STOP
---
Syntax for RISM calculation
---------------------------
Invoke of the RISM command in the main charmm input file
calls the subroutine RISM() (in rism.src). Once control has
been transferred to this subroutine the subsequent commands
are interpreted using a parser similar to the CHARMM
parser.
Main command :
RISM [NSTV int] [NSTU int] [NSOL int]
Enters the RISM module.
NSTV is the keyword to indicate the maximum number of atoms in the
solvent molecule (the default is 6 as defined in
source/fcm/rism.fcm), must be less than or equal to the default.
NSTU is for the maximum number of atoms in the solute molecule(s)
(default is 20), must be less than or equal to the default.
NSOL is for the maximum number of solutes (default is 2), the
allowed values are 1 or 2.
STOP
leaves the RISM module
Subcommands:
1) Miscellaneous commands
( compare with *note » miscom Syntax ).
GOTO
----
LABEl labelname
----
OPEN { READ { NAME filename UNIT integer } }
---- { WRITE { NAME filename UNIT integer } }
STREam [filename]
----- [ UNIT integer]
RETUrn
------
CLOSe [ UNIT integer ]
-----
SET { parameter string }
---
DECR { parameter } { BY value }
----
INCR {parameter } { BY value }
----
FORMat { format-description ((f12.5) or (e12.5) default) }
IF { parameter } { EQ } { string } ... command
-- { NE }
IF { parameter } { GT } { value } ... command
-- { GE }
{ LT }
{ LE }
2) Specific RISM commands
-------------------------
READ { PARAmeters } [show] [UNIT integer (5)]
----
{ STRUcture }
{ COORdinates {( SOLVENT )} }
{ { SOLUTE { integer (1) } } }
{ 2COOr { SOLUTE { integer (1) } } }
{ ZMATrix {(SOLVENT ) }
{ {SOLUTE { integer (1) } } }
{ 2ZMAtrix { SOLUTE { integer (1) } } }
{ CS(R) { ( VV ) }
{ [ UV [ SOLUTE integer (1) ] }
{ US(R) }
{ G(R) }
{ CH(K) [ ( VV ) ] }
{ DC(R) [ SOLUTE integer (1) ] }
{ DG(R) }
WRITe { TITLe }[ UNIT integer (6)]
-----
{ COORdinates ( SOLVENT ) }
{ { SOLUTE { (1) integer } } }
{ CS(R) { ( VV ) }
{ [ UV [ SOLUTE (1) integer ] }
{ US(R) }
{ G(R) }
{ CH(K) [ ( VV ) ] }
{ DC(R) [ SOLUTE (1) integer ] }
{ DG(R) } -
[ PLT2 ] [FROM real THRU real] [FORMAT format-spec]
{ R(I) }
{ RK(I) }
SETUp [ ( LOGFFT ) ] [ NPOINT (512) ] [ DR (0.02) ] [ RMIN (-5.12) ]
----- [ FFT ]
EDTZm [ ( SOLVENT ) ]
----- [ SOLUTE integer (1) ]
STATe [ TEMP real (300.0) ]
-----
[ DENSITY { segment-name-1 real (0.0)
... segment-name-n real (0.0) } ]
[ CDIE real (0.0) ]
ITERate { VV } \
----- { UV } only one of these options
{ UU } / -------------------------
/ [ (HNC) ]
[ PY ]
only one of these options
------------------------- [ PY2 ]
\ [ XTR { AXTR real (1.0)
RXTR1 real (0.0)
RXTR2 real (0.0)
AXTR(2) real (AXTR(1))
RXTR1(2) real (RXTR1(1))
RXTR2(2) real (RXTR2(1))
... } ]
[ INIT ] [ NCYCLE integer (1) ]
[ IUNSCR integer (0) ] [ IUNGR integer (0) ]
[ NPRINT integer (NCYCLE) ]
[ RMIX real (0.33) ] [ NDMAX integer (25) ]
[ TOL real (0.01) [ CDIE2 real (CDIE) ]
[ US(R) ]
[ G(R) ]
[ W(R) ] \
[ TS(R) ]
only one of these options
[ CAV(R)]
[ BD(R) ] /
[ SW(1) real (1.0) ]
[ SWI(1) real (SW(1)) SWF(1) real (SW(1)) DSW(1) real (0.0) ]
[ SW(2) real (1.0)]
[ SWI(2) real (SW(2)) SWF(2) real (SW(2)) DSW(2) real (0.0) ]
[ SW(3) real (1.0)] [ SWI(3) real (SW(3)) ]
[ SWI(3) real (SW(3)) SWF(3) real (SW(3)) DSW(3) real (0.0) ]
[ SW(4) real (1.0) ] [ SWI(4) real (SW(4)) ]
[ SWI(4) real (SW(4)) SWF(4) real (SW(4)) DSW(4) real (0.0) ]
DERIvative [ INIT ] [ SOLU integer (1) ]
----- [NCYCLE integer (1) ] [ NPRINT integer (NCYCLE) ]
[ RMIX real (0.33) ] [ TOL real (0.01) ]
[ CLOS (HNC) ] \
[ PY ] only one of these options
[ PY2 ] /
SOLVation { HNC } [ CHMPOT ] [ ENER ] [ CAVIT ] [ FLUC ]
-----
[ SW(1) ] [ SW(2) ] [ SW(3) ] [ SW(4) ]
[ SOLUte integer (1) ]
[ VERBO ]
[ PLT2 [ FROM real (RMIN) THRU real (RMAX) ] ]
[ UNIT integer (6) ]
ANALysis [ (VV) ]
----- [ UV ]
[ PAIR integer (all pairs) ] [ UNIT integer (6) ]
STOP
---
Top
Explanation of the RISM-specific commands
-----------------------------------------
1. Miscellaneous commads
------------------------
These commands are similar to the ones recognised by the
miscom.src routine (see note* » miscom Syntax ). We will
only mention the following differences:
a) The command OPEN should not contain the keyword CARD or FILE;
all files are opened FORMATTED
b) The command CLOSe should not be followed by a DESPosition
statement; all files are closed with DESPosition KEEP.
c) The command FORMat defines the format of the internal parameters
and should be of the form (format-specification) and up to
7 characters long (e.g. (f12.6).
2. RISM-specific commands
-------------------------
The READ command
------------------
READ PARAmeters [ show ] [ UNIT integer (5) ]
In the beginning of a RISM calculation the parameters for
the various atoms should be specified. The option show will print
into the output file the parameters for all possible atom pairs.
For all READ options one can explicitly specify an input file
from where the information will be read. If a [UNIT integer]
option is not given, the default (5) is assumed. The format for
parameter input is:
READ PARAMeters
* title
*
[COMBIne {(STANDARD)} ]
{ JORGE }
NBOND
atom-name epsilon rmin/2 charge (free format)
.....................................
END ! of NBOND
NBFIX
atom-name epsilon rmin (free format)
END ! of NBFIX
END ! of PARAMETERS
The option COMBINE STANDARD (default) uses the addition rule
for sigma's whereas JORGE uses the multiplication rule.
The epsilon value is the well depth; It can be specified positive
or negative since the code converts it to its absolute value.
==================================================================
READ STRUcture [ show ] [ UNIT integer (5) ]
This command reads the information about the atoms in the solvent
and solute molecules and the type of sites. Two sites are labeled
with the same integer only when they have the same vdw parameters
and charge AND they are geometrically equivalent. For example, in
tip3p H2O the sites for the 2 hydrogens are equivalent because
they are symetrically placed with respect to oxygen. (NOTE that if
two sites are geometrically equivalent but are given different
site index this will not affect the calculation; the opposite will
lead in erroneous results). The format of the structural input is:
READ STRUCTURE [show]
*title
*
SOLVENT
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
atom
atom atom bondlength
atom atom bondlength atom theta
atom atom bondlength atom theta atom phi
SOLUTE 1
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
.....................................................................
SOLUTE 2
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
.....................................................................
END ! of structure
The parameter NSITE should be equal to the number of atoms
in the molecule. If no specification is given the default value
NSITE=0 is assumed. NTYPE should equal the number of different sites.
If NTYPE is not specified explicitly the default value NTYPE=NSITE
is assumed.
After the line NSITE...NTYPE the various atoms are defined.
atom-1 is the (user given) name for the first atom, atom-name is the
name of this atom in the parameter list. TYPE is followed by the type
of the atom. The keywords SEGID and RESNAm specify the segment id and
the name of the residue to which the atom belongs. If the keywords
SEGID and RESNAm are not mentioned, the names SOLV, SOLU1,SOLU2 are
assumed for the solvent and the two solutes. If they are mentioned,
all atoms in the following lines are assigned to the same
SEGID and RESNAm until a line with a new explicit specification is
encountered. Notice that atoms that have different SEGID belong to
different molecules. This has the implication that the w matrix
element for those sites will be set to zero. This is useful when one
wants to define a pure solvent mixture of many components.
The atom-definition line can contain the coordinates for this
atom.The coordinate specification is important only because it allows
the program to calculate the distances between the various atoms in
the structure and construct the intramolecular matrix w. Since the
integral equation technique involves an average over all space, the
coordinates of the solvent/solute(s) and their relative location
in space (which is important in MD/MC simulations) here does not have
any other significance.
Alternatively, one can append after the atom-definition lines
the ZMATRIX description of the molecule and avoid explicit reference
to the atomic coordinates.
=====================================================================
READ COORdinates ( SOLVENT ) [ UNIT integer (5) ]
{ SOLUTE { (1) integer } }
This command allows the program to read the coordinates from
an input file in CHARMM format. The meaning of coordinates in RISM
was explained a few lines before.
======================================================================
READ 2COOr SOLUTE { 1 } integer } [UNIT integer (5) ]
This command allows the program to read the coordinates for a
second structure in CHARMM format. This second set of coordinates is
used in calculating the change in chemical potential due to a
conformational transition of the solute from the structure 1 (read by
READ COOR) into the structure 2. Note that the keyword SOLUTE must
be appended after 2COOR, otherwise the second set of coordinates
will be given to the solvent.
(see also *note » rism Theory, section 5 ).
=====================================================================
READ ZMATrix ( SOLVENT ) [ UNIT integer (5) ]
{ SOLUTE { (1) integer } }
This command reads explicitly the ZMATRIX. The format is:
READ ZMATRIX SOLVENT
* title
*
atom
atom atom bondlength
atom atom bondlength atom theta
atom atom bondlength atom theta atom phi
=====================================================================
READ 2ZMAtrix { SOLUTE { (1) integer } } [ UNIT integer (5) ]
This command reads the ZMATRIX for the second structure of
the solute. This structure is used in calculating the change in
chemical potential due to a conformational transition of the
solute from structure 1 (generated after the command READ...ZMAT
was issued) to structure 2.
(see also *note » rism Theory, section 5 ).
======================================================================
READ { CS(R) { ( VV ) } [UNIT integer]
{ [ UV [ SOLUTE (1) integer ] }
{ [ UU [ SOLUTE integer (1) ]
[ SOLUTE integer (1) ] }
{ US(R) }
{ G(R) }
This command reads the short ranged direct correlation
function cs(r), ( » rism Theory, section 2)
the short range potential us(r) (usually van der waals or whatever
the user wants to define as short-ranged, provided that it can be
fourier transformed) or the radial distribution function g(r). The
short-ranged potential us(r) should not contain the coulombic
interaction between the sites, since this is added separately
( » rism Theory, section 2)).
The various distribution functions are stored as arrays
(dvect X npair). The left index labels the point in r or k-space
and the right index labels the pair. For example, the vv csr(4,1)
stores the function for the vv pair 1 at the 4th point of the
discrete representation of space.
The format of the files where the distribution functions are
stored is the following:
* Title
NPOINT, N-DISCRETE-PAIR
SW(1) SW(2) SW(3) SW(4)
A(1,1) A(2,1) A(3,1) ... A(NPOINT,1)
A(1,2) A(2,2) A(3,2) ... A(NPOINT,2)
.....................................
The keywords VV,UV,UU define whether the input functions
refer to the solvent-solvent, solute-solvent or solute-solute
pairs respectively. If the selection is not specified the
solvent (VV) is asumed as a default. The keyword SOLUTE
specifies which solute the uv and uu functions should be
attributed to. Note that the default is SOLUTE 1 (e.g. the
command READ CS(R) UU UNIT 10) will read from unit 10 the
cs(r) and consider it as the solute 1 solute 1 function.
=====================================================================
READ CH(K) [ ( VV ) ] [ UNIT integer ]
This reads the solvent-solvent susceptibility in fourier
space. The vv susceptibility is defined as
ch(v,v',k) = w(v,v',k) + rho(v) h(v,v',k) rho(v')
(for an explanation of these symbols
» rism Theory, section 1).
=====================================================================
READ { DC(R) [ SOLUTE (1) integer ] } [UNIT integer]
{ DG(R) }
Read the derivative of the solvent-solvent direct correlation
or radial distribution function with respect to the solute density.
The keyword SOLUTE specifies which solute causes the solvent responce.
(for an explanation of these functions
» rism Theory, section 4).
=====================================================================
The WRITe command
The WRITE command is similar with the READ command. The only
additional keywords associated with the command WRITE..X (X ==
distribution function) are :
[PLT2] [FROM real THRU real ] [FORMAT format-spec]
that asks the program to print the data in columns and as a function
of the r (or k) coordinate. FROM declares the starting point for
the printing and THRU declares the last point (defaults are the
first and last point). The FORMAT is followed by a format
specification (character*80) (default is (1X,25F10.3) ). This is
different than the FORMAT command, that defines the format of the
internal parameters.
WRITE R(I) [UNIT integer]
RK(I)
will print the points in r- or k-space respectively. (see
*notes » rism Theory, Section 2).
=====================================================================
The SETUp command
SETUp { ( LOGFFT ) } [ NPOINT (512) ] [ DR (0.02) ] [ RMIN (-5.12) ]
{ FFT }
This command initializes the variables related to the fast fourier
transform that is a part of the iteration cycle (
» rism Theory, Sections 2, 3 ). The FFT on a logarithmic
scale is the default. If the keyword FFT is specified a FFT on a
linear scale will be performed (the logfft works better).
KEYWORD FUNCTION
LOGFFT The FFT on a logarithmic scale will be performed (in
the CONVEX the program uses the veclib routine).
LOGFFT is the default.
FFT Use a linear scale FFT.
NPOINT The number of points to be used in the FT (POWER OF 2)
The default is 512 which gives convergent results for
most applications with the LOGFFT. Before increasing
the number of points used, one should first
redefine the maximum number of points used (DVECT)
that is stored in rism.fcm and is currently set to
DVECT=512.
DR The spacing in r or k space
RMIN The minimum value used for the log-scale r and k-space
variables (see note* » rism Theory,
Section 2).
=====================================================================
The EDTZm command
EDTZm [ ( SOLVENT ) ]
[ SOLUTE integer (1) ]
This command edits the ZMATRIX for the solvent or solute.
The format for the command is:
EDTZm SOLVENT
ENTR integer BOND real THETA real PHI real
..................................................
END
The ENTR specifies the # of line of the original ZMATRIX
that is to be modified.
=====================================================================
The STATe command
STATe [ TEMP real (300.0) ] [ DENSITY { segment-name-1 real (0.0)
... segment-name-n real (0.0) } ] [CDIE real (0.0)]
This command allows the input of various thermodynamically
important variables. The meaning of the various keywords is:
KEYWORD FUNCTION
TEMP defines the temperature of the solution.
DENSITY defines the density of the various solvent segments.
(this is the numerical density, #of sites/A**3).
Each site in RISM is associated with a density
( » rism Theory, Section 1). Each
segment-name has been defined in the READ STRUcture
command and defines a distinct solvent molecule (in
the usual case of the one-component solvent one needs
to define one solvent segment only).
Therefore, all sites that belong to this segment will
be assigned the same density. If there are additional
solvent segments and they are not explicitly mentioned
their density will be set to zero.
CDIE defines the macroscopic dielectric constant of the
solution. This macroscopic information is needed to
correct for the asymptotic behavior of the direct
correlation functions c(r).
( » rism Theory, Sections 2, 3).
If CDIE is followed by a negative number the natural
dielectric constant is simply printed in the output,
but no adjustement of the charges is done. If CDIE
is positive the coulombic charges are adjusted so
that the long range properties of c(r) are consistent
with the CDIE given. If the keyword CDIE is omitted
no action is taken. NOTE that because the correction
assumes neutral molecules, the CDIE should not be
specified for salt solutions.
=====================================================================
The ITERate command
This is the command that starts the iteration cycle that
solves the RISM integral equations ( » rism Theory
Sections 1 and 2). Invoke of the command ITERate transfers control
to the subroutine cycles (cycles.src), which parses the command
line and calls the appropriate routines. All keywords that follow
the word ITERate should be included in the same line (lines are
appended if they end with a hyphen, as usual). The keywords used
are:
KEYWORD FUNCTION
VV Define whether the iteration cycle will solve the
UV solvent-solvent (VV) , solute-solvent (UV) or solute-
UU solute equation.
HNC Define the type of closure used (HNC is the default).
PY ( » rism Theory Section 1)
PY2 Currently the XTR closure is implemented only for the
XTR pure solvent calculation. When use XTR one should read
first the vv g(r), since this closure uses g(r) and
solves for the so called bridge function and the direct
corellation function cs(r).
INIT This keyword signifies that the cycle is initialized.
NCYCLE The maximum number of cycles to be executed.
NPRINT The frequency of printing out the change in the
direct correlation function cs(r)
TOL The tolerance that has to be satisfied in order for the
iteration loop to stop (if icycle < NCYCLE).
At each iteration step the maximum change in the function
csr (dmax) is determined and compared with the tolerance.
If dmax < tol the loop exits.
RMIX The mixing coefficient between the most recent cs(r) and
the cs(r) of the previous cycle.
( » rism Theory Section 2).
If the iteration overflows one should generally restart
the computation with larger rmix.
NDMAX The frequency of checking the dmax. In principle, the
iterations should converge by achieving gradually reduced
dmax. If the iterations start to diverge the dmax will
increase with each cycle. Every NDMAX steps the program
compares DMAX with the value stored in the previous check.
If the new dmax is found larger than before, the
coefficient RMIX is increased.
IUNCSR The unit number of the files to which cs(r) and g(r) are
IUNGR to be stored after the calculation. These keywords can
be omitted and the functions can be written to files
using explicit WRITE statements, after the iteration
loop has been completed.
CDIE2 Keyword that can be used in the UU calculation to
determine the diel. constant modifying the molecule-
molecule coulomb energy. The default CDIE value, defined
in the command STATE is otherwise used.
US(R) Determines that the short range interaction that has been
read from an input file should be used. In this case the
van der Waals parameters specified in the parameter list
are not used. This is useful if one wants to use a more
general short range potential. This option can also be
used if one wants to reconstruct the g(r) after having
determined the bridge function via the XTR closure.
NOTE that the input file should contain the potential
us(r)/KT.
G(R) Determines that the g(r) should be constructed. This
keyword is not needed in the other closures expect XTR,
since for all other cases the g(r) is automatically
constructed.
W(R) Store the potential of mean force in the auxiliary array
us(r). This can be subsequently written into a file with
the WRITE US(R)... statement.
TS(R) Store the function h-c in the auxiliary array us(r).
BD(R) Store the function us(r)/KT-bridge in the auxiliary
array us(r). If this function is read before a vv
calculation and the keywords US(R) and HNC are used,
the function g(r) (that produced the bridge) can be
reconstituted. ( » rism Theory, section 1).
CAV(R) Store the cavity term -KT*(h-c+coulomb/(cdie*KT))
in the auxiliary array us(r). This keyword is used in
the UU calculation only. The coulomb term describes the
coulomb interaction between the solute MOLECULES and is
divided by the dielectric constant cdie (that is equal
to the macroscopic dielectric defined in the command
STATE). For monoatomic solutes the term cav is equal
to the solvent-mediated interaction that the two solutes
would have if their direct coulombic interaction were
equal to coulomb/cdie. Thus, this cavity term can be
added to the CHARMM intramolecular energy for which a
cdie value has been used, to reproduce the total
vacuum + solvent-mediated molecular energy (see also
ref. [10] ).
SWI(n) The iteration loop can be executed inside a switching
SWF(n) loop that gradually switches on the interactions. This
DSW(n) prevents from numerical divergence. The integer n defines
the kind of switch used:
SW(n) n=1 - scale the total energy
n=2 - scale the sigma
n=3 - scale the coulombic charges
n=4 - scale the bridge function (used in VV only in
conjuction with the XTR closure.
SWI() defines the beginning value of the switching
coefficient, SWF() defines the final value and DSW()
the step used. One can simply specify the switching
coefficients by SW() and perform the iteration for the
particular value of SW() (without looping over the switch).
AXTR The following 6 keywords describe switching parameters
RXTR1 associated with the XTR closure and the bridge calculation
RXTR2 The switch in this case is performed with a shifting
AXTR(n) function. AXTR describes the maximum value of the
RXTR1(n) shifting function, RXTR1 the point in r-space (in A)
RXTR2(n) where the shifting function starts diminishing and RXTR2
the point where it vanishes. If the first three keywords
are used then the same values are assume for all pairs.
The explicit appearance of one of the last keywords
defines the value for the respective switch of pair n.
=====================================================================
The DERIvative command
This command starts the iteration cycle that calculates the
derivatives of the solvent-solvent g(r) and cs(r) with respect to
the solute density ( » rism Theory, Section 4 and
ref. [1]. The syntax of the command is similar to the ITERate command.
Below we explain only the keywords that differ from the ones in
the ITERate command.
KEYWORD FUNCTION
INIT Used in the beginning of the cycle to zero the dcs(r).
SOLU defines the solute, the responce to which we calculate.
(Remember that dcs(r) and dg(r) refer to solvent-solvent
quantities).
======================================================================
The SOLVation command
This command calculates the excess chemical potential of
solvation ( » rism Theory, Section 4 and [2]).
The keywords are:
KEYWORD FUNCTION
CHMPOT Calculate the chemical potential using the closed
form for the HNC-derived huv and cuv.
ENER Calculate the solute-solvent interaction energy.
This is a part of the total energy of solvation.
CAVITy Calculate the solvent reorganization energy. In
order that this term be calculated the solvent
responce dg(r) and dcs(r) must have been found
first.
FLUC Find the change in the chemical potential upon
a conformational transition of the solute (see
*note » rism Theory, Section 5).
HNC The closure used. This should be consistent with
the closure used in calculating the g(r) and cs(r).
Currently only the HNC closure is implemented for
the SOLVation calculation.
SW(i), i=1,..4 Describes the switch to which the the distribution
functions used in the calculation correspond. The
default is SW(n)=1.
VERBO Decompose the chemical potential and the interaction
energy into the contribution of the individual
solute-solvent site pairs. If the FLUC keyword
exists, then VERBO decomposes the change in chemical
potential to the contributions of the INTRAMOLECULAR
site pair terms.
PLT2 Plots the integrands in real space of the expression
FROM for the chemical potential and the interaction
THRU energy. Thus, one can get a feeling about which
terms contribute and at what distances.
UNIT Defines if another output unit than the standard
should be used.
=====================================================================
The ANALysis command
This command prints the locations of the first three maxima
and minima for the g(r) and the coordination numbers.
KEYWORD FUNCTION
VV Defines whether the vv or uv g(r) is to be printed
UV
PAIR Defines if a particular pair is to be printed
(default=all pairs).
UNIT Defines if another output unit than the standard
should be used.
=====================================================================
Explanation of the RISM-specific commands
-----------------------------------------
1. Miscellaneous commads
------------------------
These commands are similar to the ones recognised by the
miscom.src routine (see note* » miscom Syntax ). We will
only mention the following differences:
a) The command OPEN should not contain the keyword CARD or FILE;
all files are opened FORMATTED
b) The command CLOSe should not be followed by a DESPosition
statement; all files are closed with DESPosition KEEP.
c) The command FORMat defines the format of the internal parameters
and should be of the form (format-specification) and up to
7 characters long (e.g. (f12.6).
2. RISM-specific commands
-------------------------
The READ command
------------------
READ PARAmeters [ show ] [ UNIT integer (5) ]
In the beginning of a RISM calculation the parameters for
the various atoms should be specified. The option show will print
into the output file the parameters for all possible atom pairs.
For all READ options one can explicitly specify an input file
from where the information will be read. If a [UNIT integer]
option is not given, the default (5) is assumed. The format for
parameter input is:
READ PARAMeters
* title
*
[COMBIne {(STANDARD)} ]
{ JORGE }
NBOND
atom-name epsilon rmin/2 charge (free format)
.....................................
END ! of NBOND
NBFIX
atom-name epsilon rmin (free format)
END ! of NBFIX
END ! of PARAMETERS
The option COMBINE STANDARD (default) uses the addition rule
for sigma's whereas JORGE uses the multiplication rule.
The epsilon value is the well depth; It can be specified positive
or negative since the code converts it to its absolute value.
==================================================================
READ STRUcture [ show ] [ UNIT integer (5) ]
This command reads the information about the atoms in the solvent
and solute molecules and the type of sites. Two sites are labeled
with the same integer only when they have the same vdw parameters
and charge AND they are geometrically equivalent. For example, in
tip3p H2O the sites for the 2 hydrogens are equivalent because
they are symetrically placed with respect to oxygen. (NOTE that if
two sites are geometrically equivalent but are given different
site index this will not affect the calculation; the opposite will
lead in erroneous results). The format of the structural input is:
READ STRUCTURE [show]
*title
*
SOLVENT
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
atom
atom atom bondlength
atom atom bondlength atom theta
atom atom bondlength atom theta atom phi
SOLUTE 1
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
.....................................................................
SOLUTE 2
NSITE integer (0) NTYPE integer
atom-1 atom-name TYPE integer [SEGID name] [RESNAm name] [coordinates]
.....................................................................
[ZMATRIX]
.....................................................................
END ! of structure
The parameter NSITE should be equal to the number of atoms
in the molecule. If no specification is given the default value
NSITE=0 is assumed. NTYPE should equal the number of different sites.
If NTYPE is not specified explicitly the default value NTYPE=NSITE
is assumed.
After the line NSITE...NTYPE the various atoms are defined.
atom-1 is the (user given) name for the first atom, atom-name is the
name of this atom in the parameter list. TYPE is followed by the type
of the atom. The keywords SEGID and RESNAm specify the segment id and
the name of the residue to which the atom belongs. If the keywords
SEGID and RESNAm are not mentioned, the names SOLV, SOLU1,SOLU2 are
assumed for the solvent and the two solutes. If they are mentioned,
all atoms in the following lines are assigned to the same
SEGID and RESNAm until a line with a new explicit specification is
encountered. Notice that atoms that have different SEGID belong to
different molecules. This has the implication that the w matrix
element for those sites will be set to zero. This is useful when one
wants to define a pure solvent mixture of many components.
The atom-definition line can contain the coordinates for this
atom.The coordinate specification is important only because it allows
the program to calculate the distances between the various atoms in
the structure and construct the intramolecular matrix w. Since the
integral equation technique involves an average over all space, the
coordinates of the solvent/solute(s) and their relative location
in space (which is important in MD/MC simulations) here does not have
any other significance.
Alternatively, one can append after the atom-definition lines
the ZMATRIX description of the molecule and avoid explicit reference
to the atomic coordinates.
=====================================================================
READ COORdinates ( SOLVENT ) [ UNIT integer (5) ]
{ SOLUTE { (1) integer } }
This command allows the program to read the coordinates from
an input file in CHARMM format. The meaning of coordinates in RISM
was explained a few lines before.
======================================================================
READ 2COOr SOLUTE { 1 } integer } [UNIT integer (5) ]
This command allows the program to read the coordinates for a
second structure in CHARMM format. This second set of coordinates is
used in calculating the change in chemical potential due to a
conformational transition of the solute from the structure 1 (read by
READ COOR) into the structure 2. Note that the keyword SOLUTE must
be appended after 2COOR, otherwise the second set of coordinates
will be given to the solvent.
(see also *note » rism Theory, section 5 ).
=====================================================================
READ ZMATrix ( SOLVENT ) [ UNIT integer (5) ]
{ SOLUTE { (1) integer } }
This command reads explicitly the ZMATRIX. The format is:
READ ZMATRIX SOLVENT
* title
*
atom
atom atom bondlength
atom atom bondlength atom theta
atom atom bondlength atom theta atom phi
=====================================================================
READ 2ZMAtrix { SOLUTE { (1) integer } } [ UNIT integer (5) ]
This command reads the ZMATRIX for the second structure of
the solute. This structure is used in calculating the change in
chemical potential due to a conformational transition of the
solute from structure 1 (generated after the command READ...ZMAT
was issued) to structure 2.
(see also *note » rism Theory, section 5 ).
======================================================================
READ { CS(R) { ( VV ) } [UNIT integer]
{ [ UV [ SOLUTE (1) integer ] }
{ [ UU [ SOLUTE integer (1) ]
[ SOLUTE integer (1) ] }
{ US(R) }
{ G(R) }
This command reads the short ranged direct correlation
function cs(r), ( » rism Theory, section 2)
the short range potential us(r) (usually van der waals or whatever
the user wants to define as short-ranged, provided that it can be
fourier transformed) or the radial distribution function g(r). The
short-ranged potential us(r) should not contain the coulombic
interaction between the sites, since this is added separately
( » rism Theory, section 2)).
The various distribution functions are stored as arrays
(dvect X npair). The left index labels the point in r or k-space
and the right index labels the pair. For example, the vv csr(4,1)
stores the function for the vv pair 1 at the 4th point of the
discrete representation of space.
The format of the files where the distribution functions are
stored is the following:
* Title
NPOINT, N-DISCRETE-PAIR
SW(1) SW(2) SW(3) SW(4)
A(1,1) A(2,1) A(3,1) ... A(NPOINT,1)
A(1,2) A(2,2) A(3,2) ... A(NPOINT,2)
.....................................
The keywords VV,UV,UU define whether the input functions
refer to the solvent-solvent, solute-solvent or solute-solute
pairs respectively. If the selection is not specified the
solvent (VV) is asumed as a default. The keyword SOLUTE
specifies which solute the uv and uu functions should be
attributed to. Note that the default is SOLUTE 1 (e.g. the
command READ CS(R) UU UNIT 10) will read from unit 10 the
cs(r) and consider it as the solute 1 solute 1 function.
=====================================================================
READ CH(K) [ ( VV ) ] [ UNIT integer ]
This reads the solvent-solvent susceptibility in fourier
space. The vv susceptibility is defined as
ch(v,v',k) = w(v,v',k) + rho(v) h(v,v',k) rho(v')
(for an explanation of these symbols
» rism Theory, section 1).
=====================================================================
READ { DC(R) [ SOLUTE (1) integer ] } [UNIT integer]
{ DG(R) }
Read the derivative of the solvent-solvent direct correlation
or radial distribution function with respect to the solute density.
The keyword SOLUTE specifies which solute causes the solvent responce.
(for an explanation of these functions
» rism Theory, section 4).
=====================================================================
The WRITe command
The WRITE command is similar with the READ command. The only
additional keywords associated with the command WRITE..X (X ==
distribution function) are :
[PLT2] [FROM real THRU real ] [FORMAT format-spec]
that asks the program to print the data in columns and as a function
of the r (or k) coordinate. FROM declares the starting point for
the printing and THRU declares the last point (defaults are the
first and last point). The FORMAT is followed by a format
specification (character*80) (default is (1X,25F10.3) ). This is
different than the FORMAT command, that defines the format of the
internal parameters.
WRITE R(I) [UNIT integer]
RK(I)
will print the points in r- or k-space respectively. (see
*notes » rism Theory, Section 2).
=====================================================================
The SETUp command
SETUp { ( LOGFFT ) } [ NPOINT (512) ] [ DR (0.02) ] [ RMIN (-5.12) ]
{ FFT }
This command initializes the variables related to the fast fourier
transform that is a part of the iteration cycle (
» rism Theory, Sections 2, 3 ). The FFT on a logarithmic
scale is the default. If the keyword FFT is specified a FFT on a
linear scale will be performed (the logfft works better).
KEYWORD FUNCTION
LOGFFT The FFT on a logarithmic scale will be performed (in
the CONVEX the program uses the veclib routine).
LOGFFT is the default.
FFT Use a linear scale FFT.
NPOINT The number of points to be used in the FT (POWER OF 2)
The default is 512 which gives convergent results for
most applications with the LOGFFT. Before increasing
the number of points used, one should first
redefine the maximum number of points used (DVECT)
that is stored in rism.fcm and is currently set to
DVECT=512.
DR The spacing in r or k space
RMIN The minimum value used for the log-scale r and k-space
variables (see note* » rism Theory,
Section 2).
=====================================================================
The EDTZm command
EDTZm [ ( SOLVENT ) ]
[ SOLUTE integer (1) ]
This command edits the ZMATRIX for the solvent or solute.
The format for the command is:
EDTZm SOLVENT
ENTR integer BOND real THETA real PHI real
..................................................
END
The ENTR specifies the # of line of the original ZMATRIX
that is to be modified.
=====================================================================
The STATe command
STATe [ TEMP real (300.0) ] [ DENSITY { segment-name-1 real (0.0)
... segment-name-n real (0.0) } ] [CDIE real (0.0)]
This command allows the input of various thermodynamically
important variables. The meaning of the various keywords is:
KEYWORD FUNCTION
TEMP defines the temperature of the solution.
DENSITY defines the density of the various solvent segments.
(this is the numerical density, #of sites/A**3).
Each site in RISM is associated with a density
( » rism Theory, Section 1). Each
segment-name has been defined in the READ STRUcture
command and defines a distinct solvent molecule (in
the usual case of the one-component solvent one needs
to define one solvent segment only).
Therefore, all sites that belong to this segment will
be assigned the same density. If there are additional
solvent segments and they are not explicitly mentioned
their density will be set to zero.
CDIE defines the macroscopic dielectric constant of the
solution. This macroscopic information is needed to
correct for the asymptotic behavior of the direct
correlation functions c(r).
( » rism Theory, Sections 2, 3).
If CDIE is followed by a negative number the natural
dielectric constant is simply printed in the output,
but no adjustement of the charges is done. If CDIE
is positive the coulombic charges are adjusted so
that the long range properties of c(r) are consistent
with the CDIE given. If the keyword CDIE is omitted
no action is taken. NOTE that because the correction
assumes neutral molecules, the CDIE should not be
specified for salt solutions.
=====================================================================
The ITERate command
This is the command that starts the iteration cycle that
solves the RISM integral equations ( » rism Theory
Sections 1 and 2). Invoke of the command ITERate transfers control
to the subroutine cycles (cycles.src), which parses the command
line and calls the appropriate routines. All keywords that follow
the word ITERate should be included in the same line (lines are
appended if they end with a hyphen, as usual). The keywords used
are:
KEYWORD FUNCTION
VV Define whether the iteration cycle will solve the
UV solvent-solvent (VV) , solute-solvent (UV) or solute-
UU solute equation.
HNC Define the type of closure used (HNC is the default).
PY ( » rism Theory Section 1)
PY2 Currently the XTR closure is implemented only for the
XTR pure solvent calculation. When use XTR one should read
first the vv g(r), since this closure uses g(r) and
solves for the so called bridge function and the direct
corellation function cs(r).
INIT This keyword signifies that the cycle is initialized.
NCYCLE The maximum number of cycles to be executed.
NPRINT The frequency of printing out the change in the
direct correlation function cs(r)
TOL The tolerance that has to be satisfied in order for the
iteration loop to stop (if icycle < NCYCLE).
At each iteration step the maximum change in the function
csr (dmax) is determined and compared with the tolerance.
If dmax < tol the loop exits.
RMIX The mixing coefficient between the most recent cs(r) and
the cs(r) of the previous cycle.
( » rism Theory Section 2).
If the iteration overflows one should generally restart
the computation with larger rmix.
NDMAX The frequency of checking the dmax. In principle, the
iterations should converge by achieving gradually reduced
dmax. If the iterations start to diverge the dmax will
increase with each cycle. Every NDMAX steps the program
compares DMAX with the value stored in the previous check.
If the new dmax is found larger than before, the
coefficient RMIX is increased.
IUNCSR The unit number of the files to which cs(r) and g(r) are
IUNGR to be stored after the calculation. These keywords can
be omitted and the functions can be written to files
using explicit WRITE statements, after the iteration
loop has been completed.
CDIE2 Keyword that can be used in the UU calculation to
determine the diel. constant modifying the molecule-
molecule coulomb energy. The default CDIE value, defined
in the command STATE is otherwise used.
US(R) Determines that the short range interaction that has been
read from an input file should be used. In this case the
van der Waals parameters specified in the parameter list
are not used. This is useful if one wants to use a more
general short range potential. This option can also be
used if one wants to reconstruct the g(r) after having
determined the bridge function via the XTR closure.
NOTE that the input file should contain the potential
us(r)/KT.
G(R) Determines that the g(r) should be constructed. This
keyword is not needed in the other closures expect XTR,
since for all other cases the g(r) is automatically
constructed.
W(R) Store the potential of mean force in the auxiliary array
us(r). This can be subsequently written into a file with
the WRITE US(R)... statement.
TS(R) Store the function h-c in the auxiliary array us(r).
BD(R) Store the function us(r)/KT-bridge in the auxiliary
array us(r). If this function is read before a vv
calculation and the keywords US(R) and HNC are used,
the function g(r) (that produced the bridge) can be
reconstituted. ( » rism Theory, section 1).
CAV(R) Store the cavity term -KT*(h-c+coulomb/(cdie*KT))
in the auxiliary array us(r). This keyword is used in
the UU calculation only. The coulomb term describes the
coulomb interaction between the solute MOLECULES and is
divided by the dielectric constant cdie (that is equal
to the macroscopic dielectric defined in the command
STATE). For monoatomic solutes the term cav is equal
to the solvent-mediated interaction that the two solutes
would have if their direct coulombic interaction were
equal to coulomb/cdie. Thus, this cavity term can be
added to the CHARMM intramolecular energy for which a
cdie value has been used, to reproduce the total
vacuum + solvent-mediated molecular energy (see also
ref. [10] ).
SWI(n) The iteration loop can be executed inside a switching
SWF(n) loop that gradually switches on the interactions. This
DSW(n) prevents from numerical divergence. The integer n defines
the kind of switch used:
SW(n) n=1 - scale the total energy
n=2 - scale the sigma
n=3 - scale the coulombic charges
n=4 - scale the bridge function (used in VV only in
conjuction with the XTR closure.
SWI() defines the beginning value of the switching
coefficient, SWF() defines the final value and DSW()
the step used. One can simply specify the switching
coefficients by SW() and perform the iteration for the
particular value of SW() (without looping over the switch).
AXTR The following 6 keywords describe switching parameters
RXTR1 associated with the XTR closure and the bridge calculation
RXTR2 The switch in this case is performed with a shifting
AXTR(n) function. AXTR describes the maximum value of the
RXTR1(n) shifting function, RXTR1 the point in r-space (in A)
RXTR2(n) where the shifting function starts diminishing and RXTR2
the point where it vanishes. If the first three keywords
are used then the same values are assume for all pairs.
The explicit appearance of one of the last keywords
defines the value for the respective switch of pair n.
=====================================================================
The DERIvative command
This command starts the iteration cycle that calculates the
derivatives of the solvent-solvent g(r) and cs(r) with respect to
the solute density ( » rism Theory, Section 4 and
ref. [1]. The syntax of the command is similar to the ITERate command.
Below we explain only the keywords that differ from the ones in
the ITERate command.
KEYWORD FUNCTION
INIT Used in the beginning of the cycle to zero the dcs(r).
SOLU defines the solute, the responce to which we calculate.
(Remember that dcs(r) and dg(r) refer to solvent-solvent
quantities).
======================================================================
The SOLVation command
This command calculates the excess chemical potential of
solvation ( » rism Theory, Section 4 and [2]).
The keywords are:
KEYWORD FUNCTION
CHMPOT Calculate the chemical potential using the closed
form for the HNC-derived huv and cuv.
ENER Calculate the solute-solvent interaction energy.
This is a part of the total energy of solvation.
CAVITy Calculate the solvent reorganization energy. In
order that this term be calculated the solvent
responce dg(r) and dcs(r) must have been found
first.
FLUC Find the change in the chemical potential upon
a conformational transition of the solute (see
*note » rism Theory, Section 5).
HNC The closure used. This should be consistent with
the closure used in calculating the g(r) and cs(r).
Currently only the HNC closure is implemented for
the SOLVation calculation.
SW(i), i=1,..4 Describes the switch to which the the distribution
functions used in the calculation correspond. The
default is SW(n)=1.
VERBO Decompose the chemical potential and the interaction
energy into the contribution of the individual
solute-solvent site pairs. If the FLUC keyword
exists, then VERBO decomposes the change in chemical
potential to the contributions of the INTRAMOLECULAR
site pair terms.
PLT2 Plots the integrands in real space of the expression
FROM for the chemical potential and the interaction
THRU energy. Thus, one can get a feeling about which
terms contribute and at what distances.
UNIT Defines if another output unit than the standard
should be used.
=====================================================================
The ANALysis command
This command prints the locations of the first three maxima
and minima for the g(r) and the coordination numbers.
KEYWORD FUNCTION
VV Defines whether the vv or uv g(r) is to be printed
UV
PAIR Defines if a particular pair is to be printed
(default=all pairs).
UNIT Defines if another output unit than the standard
should be used.
=====================================================================
Top
A brief introduction to the RISM theory
---------------------------------------
1. The RISM equations
---------------------
A basic concept in the statistical mechanical theory of dense
systems is the radial distribution function g(r). This function
provides information about the local structure of a liquid, because
it gives the number of atoms that exist in a sphere of radius r
around any other atom via the relation:
N(r) = 4 pi r**2 rho g(r) dr (1)
where rho is the bulk density of the system. Using g(r) one can
calculate other useful quantities, such as the average interaction
energy between a solute atom and the solvent
ENER = 4 pi Integral{ r**2 rho g(r) Uuv(r) dr } (2)
where Uuv(r) is the direct interaction between the solute and the
solvent atoms at a distance r, or the excess chemical potential
dUuv(lambda)
chem. pot. = Integral { < ------- > dlambda }(3)
dlambda lambda
The radial distribution function has been assumed to depend
only on the distance r that separates two atoms. This is true for
isotropic atomic liquids, but the situation becomes more complicated
for the case of molecular liquids. In this case the interaction
between two molecules depends on their relative orientation.
Therefore, the molecular liquid radial distribution function will
depend in general not only on the distance r but also on the solid
angles that define the orientation of the molecules.
The RISM integral equation theory [3-6] assumes that molecules
can be decomposed into atomic sites. A molecular mixture can thus be
viewed as a mixture of atomic sites. Each site is surrounded by sites
of two kinds: 1) the ones that belong to the same molecule and 2) the
ones that belong to different molecules. Sites of the same molecule
are constrained to be at specific distances from each other (i.e. the
molecules are assumed to be rigid). The objective then is to
determine the g(r) between sites that belong to different molecules.
Since each site carries along a whole bunch of sites that are rigidly
separated from it, the (intermolecular pair) g(r) will depend not
only on the particular pair of sites but also on the other sites of
the two molecules.
The RISM integral equation is a matrix equation of the form:
------
rho h rho = rho w*c*w rho + rho w*c*rho h rho (4)
with rho(i) the array of atomic sites, h(i,j)=g(i,j)-1 and c(i,j)
the direct correlation function between sites i and j. The star *
denotes convolution. Eq. (4) is reminiscent of the atomic Ornstein-
Zernike equation and it can be considered as the defining
equation for c. Since it is a convolution equation, it acquires a
very simple form upon fourier transformation, becoming a product of
matricies. The matrix w has elements in Fourier space:
w(i,j) = 0 i,j in different molecules
sin(k Lij) (5)
---------- i,j in the same molecule
Lij
Thus, in r space the matrix w(i,j) is a delta function which
constrains the sites i and j to be at a distance Lij. Sites that
belong to different molecules decouple, as (5) indicates.
The array rho runs through all atomic sites of the molecular
mixture. Obviously, all atomic sites that belong to the same
molecular species have the same density (equal to the density of
the species). Equation (4) can be simplified considerably if (at
least) one molecular species (and thus all atomic sites associated
with it is considered to have zero density (this is called the
limit of infinite dilution). This assumption is made for the case
of solute-solvent and solute-solute calculations, where the solute
species is assumed to have zero density. Thus, equation (4) can
appear in one of three different forms (v denotes solVent and u
denotes solUte sites):
1) solvent-solvent
------------------
The solvent density is not zero. Dividing (4) by rho(v)*rho(v') one
gets:
h(v,v') = w(v,v')*c(v',v'')*w(v'',v)
+ w(v,v')*c(v',v'')*rho(v'')h(v'',v) (6a)
2) solute-solvent
-----------------
in this case the density of the solute sites rho(u)=0. The resulting
equation is:
h(u,v) = w(u,u')*c(u',v')*w(v',v)
+ w(u,u')*c(u',v')*rho(v')h(v',v) (6b)
The assumption rho(u)=0 prevents the intermolecular coupling of
solute-solute sites that would lead to an additional term
w(u,u')*c(u',u'')*rho(u'')h(u'',v) (7)
Thus, equation (6b) contains only the solvent-solvent distribution
function h(v',v) in the r.h.s., that can be calculated separately
in the solvent-solvent calculation.
3) solute-solute
----------------
again the solute density rho(u)=0. The solute-solute equation is:
h(u,u') = w(u,u'')*c(u'',u''')*w(u''',u')
+ w(u,u'')*c(u'',v)*rho(v)h(v,u') (6c)
As before, in the zero density limit the r.h.s contains only the solute
- solvent distribution function that can be solved separately with
equation (6b).
Equations (6a-6c) contain two unknown functions: the radial
distribution function h=g-1 and the direct correlation function c. In
order to solve them one uses a second equation (closure) that
completes the system of equations. The closures used in RISM are
inspired by the statistical mechanical theory of the atomic liquids,
where a diagrammatic analysis provides with an exact equation between
h,c and the so called "bridge function" b [3], to which equation the
various closures are approximations. The exact atomic equation is
given by:
h = exp { -u/KT +h -c +b } -1 (8)
The bridge function is unknown and thus (8) cannot be used in its
exact form. The simplest approximation is to set b=0 and get the
so called HNC closure (works better for long range interactions). In
RISM one makes the assumption that the h(a,b) between the atomic
sites a and b satisfies a closure equation identical to the atomic
case equation (8) and then one approximates (8) with one of the
following forms:
----------------------------------------------------------------------
CLOSURE EQUATION
HNC : h(a,b) = exp { -u(a,b)/KT +h(a,b) -c(a,b) } -1 (9a)
PY : h(a,b) = exp { -u(a,b)/KT } (1 +h(a,b) -c(a,b) ) -1 (9b)
PY2 : h(a,b) = exp { -u(a,b)/KT }
X (1 +h(a,b) -c(a,b) + 0.5 (h(a,b)-c(a,b))**2 ) (9c)
with a, b solvent and/or solute sites.
----------------------------------------------------------------------
Thus, the approximation made in adopting one of the above closures
with RISM is twofold: a) one extends the atomic case equation (8)
to RISM and b) one approximates further by simplifying (8).
The approximations involved and the uncertainty in the
parameters used for the potential u(a,b) result in a calculated
g(r) that does not match exactly the experimental (or MD/MC)
calculated g(r). One can follow an alternative route and use the
g(r) that results from experiment or simulations as an input in
equations (6) and (8) to determine the functions h and b. This
is referred to as the XTR closure in the RISM module. The function
-b can then be added to the short-range potential and the initial
g(r) can be reconstructed using the effective potential u-KT*b and
the HNC closure. This is similar to the Reference HNC or RHNC
method explained in [3].
2. Description of the iteration method
--------------------------------------
In order to calculate the g(r) of a molecular mixture one
defines first the solvent and the solute (if there is any)
molecular species. The solvent-solvent equation (6a) along with one
of eqs (9) is solved first. The direct correlation function c(v,v')
tends asymptotically (at large distances) to the form:
c(v,v') --> -coulomb(v,v')/KT (10)
as can be easily seen from (9). Since the solution of (6) involves
fourier transformations and the coulomb potential 1/r decreases
very slowly with distance, one separates c(v,v') in a short ranged
part cs(v,v') and a long ranged part as follows:
c(v,v') = cs(v,v') + coulomb(v,v')/KT (11)
Using this separation, the HNC (for example) closure becomes:
h(a,b) = exp { -u*(a,b)/KT +h(a,b) -cs(a,b) } -1 (9a')
with u*(a,b) the short ranged (van der Waals) interaction between a
and b. Denoting as ts the function ts = h-cs, one can write (9a') as
cs(a,b) = exp { -u*(a,b)/KT +ts(a,b) } -ts(a,b) -1 (9a'')
One can also express (6a) in terms of ts and cs. Then, one starts
with the inital guess cs(r)=0 and calculates the fourier transform of
(6a) to get ts(k). Taking the inverse F.T of ts(k) and plugging into
(9a'') one gets a new guess for csr. Then one F.T. cs(r), substitutes
into (6a) and repeats the iteration cycle until the function cs(r)
does not change more than a specified tolerance.
To decrease the numerical instability one mixes the cs(r) of
the most recent cycle (i) with the one of the previous cycle (i-1)
according to the prescription
csr = (1-rmix) csr + rmix csr (12)
i i i-1
After the solvent-solvent h(v,v') has been calculated, one
can follow the same iteration procedure to calculate the
solute-solvent h(u,v) from (6b). Subsequently, use of h(u,v) and
equation (6c) gives the solute-solute h(u,u').
The fast fourier transformation can be performed in a linear
scale, where the r-space grid is uniformly spaced, or in a
logarithmic scale (this is the default). In the latter case the grid
points are defined by the equation:
r(i) = exp { -rmin + dr (i-1) } (13)
For a description of the algorithm see [7]. The advantadge of
the log fft is that the grid is more dense at small distances, where
the distribution functions vary more rapidly. The default values used
are rmin=-5.12 and dr=0.02 giving r(1)=0.00598 and r(512)=164.02191
for 512 grid points. The log fft with these defaults has been found
to give convergent results for most of the cases.
3. Long range behavior of the RISM correlation functions
--------------------------------------------------------
As was mentioned in the previous section, the closure
equations force the site-site c(r) to decay following a coulomb law
(for charged sites). This leads to erroneous estimations of long
range properties, such as the dielectric constant. It has been
shown [8] that a simple modification of the asymptotic form for c(r)
restores the consistency with the macroscopically observed
dielectric constant. The modification is achieved by multiplying the
coulombic charges of the sites with a constant A that is site
independent and is given by the equation
1 + cdie ( 3 y -1)
A = ------------------ (14)
3 y (cdie -1)
where y is given by
4 pi rho(v)
y = ----------- (dipole**2) (15)
9 KT
and dipole denotes the dipole moment of the solvent (see also [9]).
4. Chemical potential
---------------------
After determining the solute-solvent g(r) one can calculate
the excess chemical potential of solvation using eq. (3). The
advantadge of using the HNC closure is that it provides a closed form
for the chemical potential (see ref. [2] ) :
chem. pot. = KT SUM rho(v) [ 0.5 Integral { huv**2 dV }
u,v
-0.5 Integral { huv cuv dV }
- Integral { cuv dV } ] (16)
The chemical potential can be decomposed into the energy and
entropy of solvation. The energy of solvation is a sum of two parts:
a) the solute-solvent interaction energy:
-----------------------------------------
interaction energy = SUM rho(v) [ Integral { guv Uuv dV } ] (17)
u,v
b) the cavity reorganization energy:
------------------------------------
cavity energy = SUM 0.5 rho(v)**2 [ Integral { dgvv' Uvv' dV } ](18)
v,v'
In (18) with dgvv' we denote the (of order O(rho(u))) change
in the solvent-solvent density. More specifically, the solvent-solvent
g(r) depends on the solute density. If one expresses the dependence
as a power series in the solute density:
g(v,v') = g(v,v',lambda=0) + dg(v,v') rho(u) + ... (19)
then the function dgvv' of (18) is the second term of (19). With
g(v,v',lambda=0) we denoted in (19) the solvent-solvent g(r) without
the solute present.
Since g(v,v') depends on rho(u) the solvent-solvent energy
will be slightly modified upon solvation, contributing to the
energy of solvation. As has been shown in [1], the cavity energy
persists even in the limit of infinite dilution, but it does not
contribute to the chemical potential because it is cancelled exactly
by a term in the entropy of solvation.
In order to use (18) one must of course determine the function
dgvv. This is accomplished by solving a set of equations which result
from (6) and (9) upon variation with respect to density.
To compare the resulting dgvv with the undisturbed solvent gvv
it is useful to multiply dgvv by rho(v) (as suggested by (18)).
5. Dependence of the chemical potential on the solute structure.
----------------------------------------------------------------
As was mentioned in section 1, RISM assumes that the
molecules under consideration are rigid. Upon a change in the
molecular structure the environment around a particular pair of
sites changes, modifying thus the resulting h and c functions.
This is mathematically expressed by the fact that the matrix w
appearing in (6) will change. In principle, if one is interested
to explore the dependence of the solvation chemical potential on the
solute geometry, one needs to perform a full calculation for each
solute structure. For solutes with many degrees of freedom an
exhaustive search of the conformational space can be very time
consuming. To avoid this, one can start with eqs. (6b) and (9a)
and deduce variational expressions for h, c and the matrix w.
Then, one can use the closed HNC expression for the chemical
potential to calculate the change in chemical potential upon a
conformational change from structure 1 to structure 2 as follows:
chmpot(2) - chmpot(1) = - 0.5 KT SUM Integral { c(u,v,1) x(v,v')
u,u'
c(v',u',1) (w(u,u',2)-w(u,u',1)) } (20)
As (20) indicates, one needs to perform a full RISM calculation
only once and determine the function c(u,v,1) that corresponds to
a particular structure 1. Then, to estimate the potential of any
structure 2 one only needs to supply (20) with the new coordinates.
Note that (20) is a sum over intramolecular site pairs, in contrast
to the expression for the chemical potential. Each term of the
sum gives the contribution to the change in chemical potential of
the corresponding pair of sites in the structure. By comparing
these terms one can conclude which parts of the structure are
mostly responsible for the change in chemical potential.
A brief introduction to the RISM theory
---------------------------------------
1. The RISM equations
---------------------
A basic concept in the statistical mechanical theory of dense
systems is the radial distribution function g(r). This function
provides information about the local structure of a liquid, because
it gives the number of atoms that exist in a sphere of radius r
around any other atom via the relation:
N(r) = 4 pi r**2 rho g(r) dr (1)
where rho is the bulk density of the system. Using g(r) one can
calculate other useful quantities, such as the average interaction
energy between a solute atom and the solvent
ENER = 4 pi Integral{ r**2 rho g(r) Uuv(r) dr } (2)
where Uuv(r) is the direct interaction between the solute and the
solvent atoms at a distance r, or the excess chemical potential
dUuv(lambda)
chem. pot. = Integral { < ------- > dlambda }(3)
dlambda lambda
The radial distribution function has been assumed to depend
only on the distance r that separates two atoms. This is true for
isotropic atomic liquids, but the situation becomes more complicated
for the case of molecular liquids. In this case the interaction
between two molecules depends on their relative orientation.
Therefore, the molecular liquid radial distribution function will
depend in general not only on the distance r but also on the solid
angles that define the orientation of the molecules.
The RISM integral equation theory [3-6] assumes that molecules
can be decomposed into atomic sites. A molecular mixture can thus be
viewed as a mixture of atomic sites. Each site is surrounded by sites
of two kinds: 1) the ones that belong to the same molecule and 2) the
ones that belong to different molecules. Sites of the same molecule
are constrained to be at specific distances from each other (i.e. the
molecules are assumed to be rigid). The objective then is to
determine the g(r) between sites that belong to different molecules.
Since each site carries along a whole bunch of sites that are rigidly
separated from it, the (intermolecular pair) g(r) will depend not
only on the particular pair of sites but also on the other sites of
the two molecules.
The RISM integral equation is a matrix equation of the form:
------
rho h rho = rho w*c*w rho + rho w*c*rho h rho (4)
with rho(i) the array of atomic sites, h(i,j)=g(i,j)-1 and c(i,j)
the direct correlation function between sites i and j. The star *
denotes convolution. Eq. (4) is reminiscent of the atomic Ornstein-
Zernike equation and it can be considered as the defining
equation for c. Since it is a convolution equation, it acquires a
very simple form upon fourier transformation, becoming a product of
matricies. The matrix w has elements in Fourier space:
w(i,j) = 0 i,j in different molecules
sin(k Lij) (5)
---------- i,j in the same molecule
Lij
Thus, in r space the matrix w(i,j) is a delta function which
constrains the sites i and j to be at a distance Lij. Sites that
belong to different molecules decouple, as (5) indicates.
The array rho runs through all atomic sites of the molecular
mixture. Obviously, all atomic sites that belong to the same
molecular species have the same density (equal to the density of
the species). Equation (4) can be simplified considerably if (at
least) one molecular species (and thus all atomic sites associated
with it is considered to have zero density (this is called the
limit of infinite dilution). This assumption is made for the case
of solute-solvent and solute-solute calculations, where the solute
species is assumed to have zero density. Thus, equation (4) can
appear in one of three different forms (v denotes solVent and u
denotes solUte sites):
1) solvent-solvent
------------------
The solvent density is not zero. Dividing (4) by rho(v)*rho(v') one
gets:
h(v,v') = w(v,v')*c(v',v'')*w(v'',v)
+ w(v,v')*c(v',v'')*rho(v'')h(v'',v) (6a)
2) solute-solvent
-----------------
in this case the density of the solute sites rho(u)=0. The resulting
equation is:
h(u,v) = w(u,u')*c(u',v')*w(v',v)
+ w(u,u')*c(u',v')*rho(v')h(v',v) (6b)
The assumption rho(u)=0 prevents the intermolecular coupling of
solute-solute sites that would lead to an additional term
w(u,u')*c(u',u'')*rho(u'')h(u'',v) (7)
Thus, equation (6b) contains only the solvent-solvent distribution
function h(v',v) in the r.h.s., that can be calculated separately
in the solvent-solvent calculation.
3) solute-solute
----------------
again the solute density rho(u)=0. The solute-solute equation is:
h(u,u') = w(u,u'')*c(u'',u''')*w(u''',u')
+ w(u,u'')*c(u'',v)*rho(v)h(v,u') (6c)
As before, in the zero density limit the r.h.s contains only the solute
- solvent distribution function that can be solved separately with
equation (6b).
Equations (6a-6c) contain two unknown functions: the radial
distribution function h=g-1 and the direct correlation function c. In
order to solve them one uses a second equation (closure) that
completes the system of equations. The closures used in RISM are
inspired by the statistical mechanical theory of the atomic liquids,
where a diagrammatic analysis provides with an exact equation between
h,c and the so called "bridge function" b [3], to which equation the
various closures are approximations. The exact atomic equation is
given by:
h = exp { -u/KT +h -c +b } -1 (8)
The bridge function is unknown and thus (8) cannot be used in its
exact form. The simplest approximation is to set b=0 and get the
so called HNC closure (works better for long range interactions). In
RISM one makes the assumption that the h(a,b) between the atomic
sites a and b satisfies a closure equation identical to the atomic
case equation (8) and then one approximates (8) with one of the
following forms:
----------------------------------------------------------------------
CLOSURE EQUATION
HNC : h(a,b) = exp { -u(a,b)/KT +h(a,b) -c(a,b) } -1 (9a)
PY : h(a,b) = exp { -u(a,b)/KT } (1 +h(a,b) -c(a,b) ) -1 (9b)
PY2 : h(a,b) = exp { -u(a,b)/KT }
X (1 +h(a,b) -c(a,b) + 0.5 (h(a,b)-c(a,b))**2 ) (9c)
with a, b solvent and/or solute sites.
----------------------------------------------------------------------
Thus, the approximation made in adopting one of the above closures
with RISM is twofold: a) one extends the atomic case equation (8)
to RISM and b) one approximates further by simplifying (8).
The approximations involved and the uncertainty in the
parameters used for the potential u(a,b) result in a calculated
g(r) that does not match exactly the experimental (or MD/MC)
calculated g(r). One can follow an alternative route and use the
g(r) that results from experiment or simulations as an input in
equations (6) and (8) to determine the functions h and b. This
is referred to as the XTR closure in the RISM module. The function
-b can then be added to the short-range potential and the initial
g(r) can be reconstructed using the effective potential u-KT*b and
the HNC closure. This is similar to the Reference HNC or RHNC
method explained in [3].
2. Description of the iteration method
--------------------------------------
In order to calculate the g(r) of a molecular mixture one
defines first the solvent and the solute (if there is any)
molecular species. The solvent-solvent equation (6a) along with one
of eqs (9) is solved first. The direct correlation function c(v,v')
tends asymptotically (at large distances) to the form:
c(v,v') --> -coulomb(v,v')/KT (10)
as can be easily seen from (9). Since the solution of (6) involves
fourier transformations and the coulomb potential 1/r decreases
very slowly with distance, one separates c(v,v') in a short ranged
part cs(v,v') and a long ranged part as follows:
c(v,v') = cs(v,v') + coulomb(v,v')/KT (11)
Using this separation, the HNC (for example) closure becomes:
h(a,b) = exp { -u*(a,b)/KT +h(a,b) -cs(a,b) } -1 (9a')
with u*(a,b) the short ranged (van der Waals) interaction between a
and b. Denoting as ts the function ts = h-cs, one can write (9a') as
cs(a,b) = exp { -u*(a,b)/KT +ts(a,b) } -ts(a,b) -1 (9a'')
One can also express (6a) in terms of ts and cs. Then, one starts
with the inital guess cs(r)=0 and calculates the fourier transform of
(6a) to get ts(k). Taking the inverse F.T of ts(k) and plugging into
(9a'') one gets a new guess for csr. Then one F.T. cs(r), substitutes
into (6a) and repeats the iteration cycle until the function cs(r)
does not change more than a specified tolerance.
To decrease the numerical instability one mixes the cs(r) of
the most recent cycle (i) with the one of the previous cycle (i-1)
according to the prescription
csr = (1-rmix) csr + rmix csr (12)
i i i-1
After the solvent-solvent h(v,v') has been calculated, one
can follow the same iteration procedure to calculate the
solute-solvent h(u,v) from (6b). Subsequently, use of h(u,v) and
equation (6c) gives the solute-solute h(u,u').
The fast fourier transformation can be performed in a linear
scale, where the r-space grid is uniformly spaced, or in a
logarithmic scale (this is the default). In the latter case the grid
points are defined by the equation:
r(i) = exp { -rmin + dr (i-1) } (13)
For a description of the algorithm see [7]. The advantadge of
the log fft is that the grid is more dense at small distances, where
the distribution functions vary more rapidly. The default values used
are rmin=-5.12 and dr=0.02 giving r(1)=0.00598 and r(512)=164.02191
for 512 grid points. The log fft with these defaults has been found
to give convergent results for most of the cases.
3. Long range behavior of the RISM correlation functions
--------------------------------------------------------
As was mentioned in the previous section, the closure
equations force the site-site c(r) to decay following a coulomb law
(for charged sites). This leads to erroneous estimations of long
range properties, such as the dielectric constant. It has been
shown [8] that a simple modification of the asymptotic form for c(r)
restores the consistency with the macroscopically observed
dielectric constant. The modification is achieved by multiplying the
coulombic charges of the sites with a constant A that is site
independent and is given by the equation
1 + cdie ( 3 y -1)
A = ------------------ (14)
3 y (cdie -1)
where y is given by
4 pi rho(v)
y = ----------- (dipole**2) (15)
9 KT
and dipole denotes the dipole moment of the solvent (see also [9]).
4. Chemical potential
---------------------
After determining the solute-solvent g(r) one can calculate
the excess chemical potential of solvation using eq. (3). The
advantadge of using the HNC closure is that it provides a closed form
for the chemical potential (see ref. [2] ) :
chem. pot. = KT SUM rho(v) [ 0.5 Integral { huv**2 dV }
u,v
-0.5 Integral { huv cuv dV }
- Integral { cuv dV } ] (16)
The chemical potential can be decomposed into the energy and
entropy of solvation. The energy of solvation is a sum of two parts:
a) the solute-solvent interaction energy:
-----------------------------------------
interaction energy = SUM rho(v) [ Integral { guv Uuv dV } ] (17)
u,v
b) the cavity reorganization energy:
------------------------------------
cavity energy = SUM 0.5 rho(v)**2 [ Integral { dgvv' Uvv' dV } ](18)
v,v'
In (18) with dgvv' we denote the (of order O(rho(u))) change
in the solvent-solvent density. More specifically, the solvent-solvent
g(r) depends on the solute density. If one expresses the dependence
as a power series in the solute density:
g(v,v') = g(v,v',lambda=0) + dg(v,v') rho(u) + ... (19)
then the function dgvv' of (18) is the second term of (19). With
g(v,v',lambda=0) we denoted in (19) the solvent-solvent g(r) without
the solute present.
Since g(v,v') depends on rho(u) the solvent-solvent energy
will be slightly modified upon solvation, contributing to the
energy of solvation. As has been shown in [1], the cavity energy
persists even in the limit of infinite dilution, but it does not
contribute to the chemical potential because it is cancelled exactly
by a term in the entropy of solvation.
In order to use (18) one must of course determine the function
dgvv. This is accomplished by solving a set of equations which result
from (6) and (9) upon variation with respect to density.
To compare the resulting dgvv with the undisturbed solvent gvv
it is useful to multiply dgvv by rho(v) (as suggested by (18)).
5. Dependence of the chemical potential on the solute structure.
----------------------------------------------------------------
As was mentioned in section 1, RISM assumes that the
molecules under consideration are rigid. Upon a change in the
molecular structure the environment around a particular pair of
sites changes, modifying thus the resulting h and c functions.
This is mathematically expressed by the fact that the matrix w
appearing in (6) will change. In principle, if one is interested
to explore the dependence of the solvation chemical potential on the
solute geometry, one needs to perform a full calculation for each
solute structure. For solutes with many degrees of freedom an
exhaustive search of the conformational space can be very time
consuming. To avoid this, one can start with eqs. (6b) and (9a)
and deduce variational expressions for h, c and the matrix w.
Then, one can use the closed HNC expression for the chemical
potential to calculate the change in chemical potential upon a
conformational change from structure 1 to structure 2 as follows:
chmpot(2) - chmpot(1) = - 0.5 KT SUM Integral { c(u,v,1) x(v,v')
u,u'
c(v',u',1) (w(u,u',2)-w(u,u',1)) } (20)
As (20) indicates, one needs to perform a full RISM calculation
only once and determine the function c(u,v,1) that corresponds to
a particular structure 1. Then, to estimate the potential of any
structure 2 one only needs to supply (20) with the new coordinates.
Note that (20) is a sum over intramolecular site pairs, in contrast
to the expression for the chemical potential. Each term of the
sum gives the contribution to the change in chemical potential of
the corresponding pair of sites in the structure. By comparing
these terms one can conclude which parts of the structure are
mostly responsible for the change in chemical potential.
Top
References
----------
[1] H. A. Yu, and M. Karplus, JCP (1988) 89, 2366-2379. A
thermodynamic analysis of solvation.
[2] S.J. Singer and D. Chandler, Mol. Phys. (1985), 55, 621-625.
Free energy functions in the extended RISM approximation.
[3] J. P. Hansen and I. R. Mcdonald, Theory of Simple Liquids, 2nd Edition,
Academic Press, (1986).
[4] D. Chandler, The liquid state of matter: Fluids, simple and
complex. E.W. Montroll and J.L. Lebowitz (editors), North Holland
Publishing Company, 1982, 275-340.
[5] F. Hirata and P.J. Rossky, Chem. Phys. Lett. (1981) 83, 329-334.
An extended RISM equation for molecular polar fluids.
[6] F. Hirata, P.J. Rossky and M. B. Pettitt, JCP (1983), 78, 4133-4144.
The interionic potential of mean force in a molecular polar
solvent from an extended RISM equation.
[7] P. J. Rossky and H. L. Freedman, JCP (1980), 72, 5694.
Accurate solutions to integral equations describing weakly
screened ionic systems.
[8] P. J. Rossky, M. B. Pettitt and G. Stell, Mol. Phys. (1983), 50, 1263-1267.
The coupling of long and short range correlations in ISM liquids.
[9] D. Chandler, JCP (1977), 67, 1113-1124. The dielectric constant
and related equilibrium properties of molecular fluids:
Interaction site cluster theory analysis.
[10] M. B. Pettitt, M. Karplus and P. J. Rossky, JPC (1986), 90, 6335-6345.
Integral equation model for aqueous solvation of polyatomic
solutes: Application to the determination of the free energy
surface for the internal motion of biomolecules.
[11] H. A. Yu, B. Roux and M. Karplus, JCP (1990) 92, 5020-5033.
Solvation thermodynamics: An approach from analytic temperature
derivatives.
References
----------
[1] H. A. Yu, and M. Karplus, JCP (1988) 89, 2366-2379. A
thermodynamic analysis of solvation.
[2] S.J. Singer and D. Chandler, Mol. Phys. (1985), 55, 621-625.
Free energy functions in the extended RISM approximation.
[3] J. P. Hansen and I. R. Mcdonald, Theory of Simple Liquids, 2nd Edition,
Academic Press, (1986).
[4] D. Chandler, The liquid state of matter: Fluids, simple and
complex. E.W. Montroll and J.L. Lebowitz (editors), North Holland
Publishing Company, 1982, 275-340.
[5] F. Hirata and P.J. Rossky, Chem. Phys. Lett. (1981) 83, 329-334.
An extended RISM equation for molecular polar fluids.
[6] F. Hirata, P.J. Rossky and M. B. Pettitt, JCP (1983), 78, 4133-4144.
The interionic potential of mean force in a molecular polar
solvent from an extended RISM equation.
[7] P. J. Rossky and H. L. Freedman, JCP (1980), 72, 5694.
Accurate solutions to integral equations describing weakly
screened ionic systems.
[8] P. J. Rossky, M. B. Pettitt and G. Stell, Mol. Phys. (1983), 50, 1263-1267.
The coupling of long and short range correlations in ISM liquids.
[9] D. Chandler, JCP (1977), 67, 1113-1124. The dielectric constant
and related equilibrium properties of molecular fluids:
Interaction site cluster theory analysis.
[10] M. B. Pettitt, M. Karplus and P. J. Rossky, JPC (1986), 90, 6335-6345.
Integral equation model for aqueous solvation of polyatomic
solutes: Application to the determination of the free energy
surface for the internal motion of biomolecules.
[11] H. A. Yu, B. Roux and M. Karplus, JCP (1990) 92, 5020-5033.
Solvation thermodynamics: An approach from analytic temperature
derivatives.
Top
Input files : 1) vv calculation
2) uv
uu
derivative
---------------------------------------------------------------------
FIRST INPUT FILE
---------------------------------------------------------------------
* CHARMM input file for the RISM calculations
* test the pure solvent calculation
* use tip3p water as solvent
! enter the RISM module
RISM
! read the parameters
read parameters show
* PARAMETERS for RISM (from CHARMM)
NBOND
! Solvent:
! epsilon Rmin/2 Charge
! epsilon needs not be given as negative
!
OT 0.1591 1.60000 -0.834
HT 0.0498 0.80000 0.417
NH1 0.23840 1.60000 -0.350 ! NH1
H 0.04980 0.80000 0.250 ! H
CH1E 0.04860 2.36500 0.100 ! CH1E
CH31 0.18110 2.16500 0.100 ! CH3E
C -0.12000 2.10000 0.550 ! C
O -0.15910 1.60000 -0.550 ! O
CH32 -0.18110 2.16500 -0.100 ! CH3E
CH4 -0.294 2.09300 0.00
END
! the list of specific solute-solvent pairs:
NBFIX
!Solvent molecule
! epsilon Rmin
!
OT OT -0.15207 3.53650
HT OT -0.08363 1.99270
HT HT -0.04598 0.44900
END ! (of NBFIX)
END ! (of parameters)
! now read the strucutre
read structure show
* structure for the solvent
! read the type of solvent sites
solvent
nsite 3 ntype 2
OT OT type 1 segid BULK resnam TIP3
HT1 HT type 2
HT2 HT type 2
! and its geometry via a ZMATRIX
ZMATRIX
OT
HT1 OT 0.9572
HT2 OT 0.9572 HT1 104.52
END
! define the temperature, the density and the macroscopic dielectric
! constant
state temp 298.15 density BULK 0.03334 cdie 78.6
! start the iteration cycle to calculate the vv cs(r) and g(r)
iterate vv hnc ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.10 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate vv hnc ncycle 500 nprint 1 -
swi(1) 0.1 swf(1) 1.0 dsw(1) 0.1 -
tol 0.9 rmix 0.39
iterate vv hnc ncycle 5000 nprint 10 -
tol 0.00001 rmix 0.39
! print out the characteristics of g(r) for pair 1
analysis vv pair 1
! now for all pairs
analysis vv
! write the calculated distribution functions
! first cs(r)
open write name tip3p-charmm.csr unit 20
write cs(r) vv unit 20
* cs(r) for tip3p calculated with the charmm executable
close unit 20
! then g(r)
open write name tip3p-charmm.gr unit 20
write g(r) vv unit 20
* g(r) for tip3p water with the charmm-prepared executable
close unit 20
! write the g(r) in formmatted form as a function of distance
open write name tip3p-charmm-plt2.gr unit 20
write g(r) vv plt2 all from 0.5 thru 10.0 format(1x,10f10.5) unit 20
* g(r) for water with the charmm-prepared executable
* r(i) O-O O-H H-H
close unit 20
! exit RISM
stop
! exit CHARMM
stop
!---------------------------------------------------------------------
SECOND INPUT FILE
----------------------------------------------------------------------
* input test file for the uv calculation
* the uu calculation
* the derivative calculation
! enter the RISM module
RISM NSTV 3 NSTU 2 NSOL 2
! test the solute-solvent cs(r) and g(r) calculation
! use tip3p water as solvent
! read first the parameters; show will produce a detailed output
read parameters show
* PARAMETERS for RISM (from CHARMM)
NBOND
! Solvent:
! epsilon Rmin/2 charge
!
OT -0.1591 1.60000 -0.834
HT -0.0498 0.80000 0.417
NH1 -0.23840 1.60000 -0.350 ! NH1
H -0.04980 0.80000 0.250 ! H
CH1E -0.04860 2.36500 0.100 ! CH1E
CH31 -0.18110 2.16500 0.100 ! CH3E
C -0.12000 2.10000 0.550 ! C
O -0.15910 1.60000 -0.550 ! O
CH32 -0.18110 2.16500 -0.100 ! CH3E
CH4 -0.294 2.09300 0.00
END
! the list of specific solvent-solvent pairs:
NBFIX
!Solvent molecule
! epsilon Rmin
!
OT OT -0.15207 3.53650
HT OT -0.08363 1.99270
HT HT -0.04598 0.44900
END ! (of NBFIX)
END ! (of parameters)
read structure show
* tip3p as solvent
! read first the type of solvent sites
SOLVENT
nsite 3 ntype 2
OT OT type 1 segid BULK resnam TIP3
HT1 HT type 2
HT2 HT type 2
! and the solvent geometry
ZMATRIX
OT
HT1 OT 0.9572
HT2 OT 0.9572 HT1 104.52
! now do the same for the solutes
! monoatomic molecules do not need a ZMATRIX since they do not have
! any geometry
SOLUTE 1
nsite 1 ntype 1
CH31 CH31 type 1 segid SOLU resnam SOLU
!
! solute 2 is CH1E-CH1E, thus the two sites are of the same type
SOLUTE 2
nsite 2 ntype 2
C1 CH31 type 1 segid SLU2 resnam SLU2
C2 CH32 type 1
ZMATRIX
C1
C2 C1 4.0
END
! read the state (temperature, solvent density and cdie)
state temp 298.15 density BULK 0.03334 cdie 78.6
! read the converged cs(r) for the solvent-solvent (calculated
! before).
open read unit 20 name tip3p-charmm.csr
read cs(r) vv unit 20
close unit 20
! iterate a few steps to check the convergence
! and generate the solvent-solvent g(r)
iterate vv hnc ncycle 500 nprint 10 -
tol 0.00001 rmix 0.39
! now do the uv (solVent-solUte) calculation
iterate uv hnc solute 1 ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 1 hnc ncycle 500 nprint 1 -
swi(1) 0.1 swf(1) 1.0 dsw(1) 0.1 -
tol 0.9 rmix 0.39
iterate uv solute 1 hnc ncycle 5000 nprint 10 -
tol 0.001 rmix 0.39
! print out the solute-solvent g(r) characteristics
analysis uv solute 1
! write in files the distribution functions for the solute-solvent
! site pairs
open write name soluv1-charmm.csr unit 20
write cs(r) uv solute 1 unit 20
* cs(r) for CH31 into water with the charmm-prepared executable
close unit 20
open write name soluv1-charmm.gr unit 20
write g(r) uv solute 1 unit 20
* g(r) for CH31 into water with the charmm-prepared executable
close unit 20
open write name soluv1-charmm-plt2.gr unit 20
write g(r) uv solute 1 plt2 all from 0.5 thru 10.0 -
format(1x,10f10.5) unit 20
* g(r) for CH31 into tip3p water with the charmm-prepared executable
close unit 20
! calculate the chemical potential and the solute-solvent
! interaction energy. The cavity energy cannot be calculated
! bewcause we have not done the derivative calculation.
solvation chmpot energy plt2 verbose solute 1
! ===================================================================
! now do the second solute calculation
------------------------------------
iterate uv hnc solute 2 ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 2 hnc ncycle 500 nprint 1 -
swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 2 hnc ncycle 5000 nprint 10 -
tol 0.001 rmix 0.39
! print out the solute-solvent g(r) characteristics
analysis uv solute 2
! write in files the distribution functions for the solute-solvent
! site pairs
open write name soluv2-charmm.csr unit 20
write cs(r) uv solute 2 unit 20
* cs(r) for CH31-CH32 into water with the charmm-prepared executable
close unit 20
open write name soluv2-charmm.gr unit 20
write g(r) uv solute 2 unit 20
* g(r) for CH31-CH32 into water with the charmm-prepared executable
close unit 20
open write name soluv2-charmm-plt2.gr unit 20
write g(r) uv solute 2 plt2 all from 0.5 thru 10.0 -
format(1x,10f10.5) unit 20
* g(r) for CH31-CH32 into tip3p water with the charmm-prepared executable
close unit 20
! calculate the chemical potential and the solute-solvent
! interaction energy
solvation chmpot energy plt2 verbose solute 2
! ===================================================================
! now do the solute 1 - solute 2 calculation
! store the potential of mean force in us(r)
iterate uu hnc w(r) solute 1 solute 2 ncycle 500 nprint 1 -
init tol 0.001 rmix 0.29
open write name sol1-sol2.pmf unit 20
write us(r) uu solute 1 solute 2 unit 20
* pmf for the solutes CH3E and CH31-CH32
close unit 20
open write name sol1-sol2.csr unit 20
write cs(r) uu solute 1 solute 2 unit 20
* cs(r) for the solutes CH3E and CH31-CH32
close unit 20
! ===================================================================
! now do the DERIVATIVE calculation
! test the calculation of the responce of the solvent to the
! solvation of a solute moleculte (infinite dilution)
! use tip3p water as solvent
! first for the solute 1
derivative hnc solute 1 ncycle 5000 nprint 1 -
init tol 0.001 rmix 0.39
open write name tip3p-uv1-charmm.dcsr unit 30
write dc(r) solute 1 unit 30
* derivative of cs(r) of tip3p upon solvation of CH31
close unit 30
open write name tip3p-uv1-charmm.dgr unit 30
write dg(r) solute 1 unit 30
* derivative of g(r) of tip3p upon solvation of CH31
close unit 30
! calculate the chemical potential, the interaction energy
! and the cavity formation energy
solvation chmpot energy cavity solute 1 verbose
! now do the calculation for solute 2
derivative hnc solute 2 ncycle 5000 nprint 1 -
init tol 0.001 rmix 0.39
open write name tip3p-uv2-charmm.dcsr unit 30
write dc(r) solute 2 unit 30
* derivative of cs(r) of tip3p upon solvation of CH31-CH32
close unit 30
open write name tip3p-uv2-charmm.dgr unit 30
write dg(r) solute 2 unit 30
* derivative of g(r) of tip3p upon solvation of CH31-CH32
close unit 30
! calculate the chemical potential, the interaction energy
! and the cavity formation energy
solvation chmpot energy cavity solute 2 verbose
!exit RISM
stop
!exit CHARMM
stop
----------------------------------------------------------------------
Input files : 1) vv calculation
2) uv
uu
derivative
---------------------------------------------------------------------
FIRST INPUT FILE
---------------------------------------------------------------------
* CHARMM input file for the RISM calculations
* test the pure solvent calculation
* use tip3p water as solvent
! enter the RISM module
RISM
! read the parameters
read parameters show
* PARAMETERS for RISM (from CHARMM)
NBOND
! Solvent:
! epsilon Rmin/2 Charge
! epsilon needs not be given as negative
!
OT 0.1591 1.60000 -0.834
HT 0.0498 0.80000 0.417
NH1 0.23840 1.60000 -0.350 ! NH1
H 0.04980 0.80000 0.250 ! H
CH1E 0.04860 2.36500 0.100 ! CH1E
CH31 0.18110 2.16500 0.100 ! CH3E
C -0.12000 2.10000 0.550 ! C
O -0.15910 1.60000 -0.550 ! O
CH32 -0.18110 2.16500 -0.100 ! CH3E
CH4 -0.294 2.09300 0.00
END
! the list of specific solute-solvent pairs:
NBFIX
!Solvent molecule
! epsilon Rmin
!
OT OT -0.15207 3.53650
HT OT -0.08363 1.99270
HT HT -0.04598 0.44900
END ! (of NBFIX)
END ! (of parameters)
! now read the strucutre
read structure show
* structure for the solvent
! read the type of solvent sites
solvent
nsite 3 ntype 2
OT OT type 1 segid BULK resnam TIP3
HT1 HT type 2
HT2 HT type 2
! and its geometry via a ZMATRIX
ZMATRIX
OT
HT1 OT 0.9572
HT2 OT 0.9572 HT1 104.52
END
! define the temperature, the density and the macroscopic dielectric
! constant
state temp 298.15 density BULK 0.03334 cdie 78.6
! start the iteration cycle to calculate the vv cs(r) and g(r)
iterate vv hnc ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.10 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate vv hnc ncycle 500 nprint 1 -
swi(1) 0.1 swf(1) 1.0 dsw(1) 0.1 -
tol 0.9 rmix 0.39
iterate vv hnc ncycle 5000 nprint 10 -
tol 0.00001 rmix 0.39
! print out the characteristics of g(r) for pair 1
analysis vv pair 1
! now for all pairs
analysis vv
! write the calculated distribution functions
! first cs(r)
open write name tip3p-charmm.csr unit 20
write cs(r) vv unit 20
* cs(r) for tip3p calculated with the charmm executable
close unit 20
! then g(r)
open write name tip3p-charmm.gr unit 20
write g(r) vv unit 20
* g(r) for tip3p water with the charmm-prepared executable
close unit 20
! write the g(r) in formmatted form as a function of distance
open write name tip3p-charmm-plt2.gr unit 20
write g(r) vv plt2 all from 0.5 thru 10.0 format(1x,10f10.5) unit 20
* g(r) for water with the charmm-prepared executable
* r(i) O-O O-H H-H
close unit 20
! exit RISM
stop
! exit CHARMM
stop
!---------------------------------------------------------------------
SECOND INPUT FILE
----------------------------------------------------------------------
* input test file for the uv calculation
* the uu calculation
* the derivative calculation
! enter the RISM module
RISM NSTV 3 NSTU 2 NSOL 2
! test the solute-solvent cs(r) and g(r) calculation
! use tip3p water as solvent
! read first the parameters; show will produce a detailed output
read parameters show
* PARAMETERS for RISM (from CHARMM)
NBOND
! Solvent:
! epsilon Rmin/2 charge
!
OT -0.1591 1.60000 -0.834
HT -0.0498 0.80000 0.417
NH1 -0.23840 1.60000 -0.350 ! NH1
H -0.04980 0.80000 0.250 ! H
CH1E -0.04860 2.36500 0.100 ! CH1E
CH31 -0.18110 2.16500 0.100 ! CH3E
C -0.12000 2.10000 0.550 ! C
O -0.15910 1.60000 -0.550 ! O
CH32 -0.18110 2.16500 -0.100 ! CH3E
CH4 -0.294 2.09300 0.00
END
! the list of specific solvent-solvent pairs:
NBFIX
!Solvent molecule
! epsilon Rmin
!
OT OT -0.15207 3.53650
HT OT -0.08363 1.99270
HT HT -0.04598 0.44900
END ! (of NBFIX)
END ! (of parameters)
read structure show
* tip3p as solvent
! read first the type of solvent sites
SOLVENT
nsite 3 ntype 2
OT OT type 1 segid BULK resnam TIP3
HT1 HT type 2
HT2 HT type 2
! and the solvent geometry
ZMATRIX
OT
HT1 OT 0.9572
HT2 OT 0.9572 HT1 104.52
! now do the same for the solutes
! monoatomic molecules do not need a ZMATRIX since they do not have
! any geometry
SOLUTE 1
nsite 1 ntype 1
CH31 CH31 type 1 segid SOLU resnam SOLU
!
! solute 2 is CH1E-CH1E, thus the two sites are of the same type
SOLUTE 2
nsite 2 ntype 2
C1 CH31 type 1 segid SLU2 resnam SLU2
C2 CH32 type 1
ZMATRIX
C1
C2 C1 4.0
END
! read the state (temperature, solvent density and cdie)
state temp 298.15 density BULK 0.03334 cdie 78.6
! read the converged cs(r) for the solvent-solvent (calculated
! before).
open read unit 20 name tip3p-charmm.csr
read cs(r) vv unit 20
close unit 20
! iterate a few steps to check the convergence
! and generate the solvent-solvent g(r)
iterate vv hnc ncycle 500 nprint 10 -
tol 0.00001 rmix 0.39
! now do the uv (solVent-solUte) calculation
iterate uv hnc solute 1 ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 1 hnc ncycle 500 nprint 1 -
swi(1) 0.1 swf(1) 1.0 dsw(1) 0.1 -
tol 0.9 rmix 0.39
iterate uv solute 1 hnc ncycle 5000 nprint 10 -
tol 0.001 rmix 0.39
! print out the solute-solvent g(r) characteristics
analysis uv solute 1
! write in files the distribution functions for the solute-solvent
! site pairs
open write name soluv1-charmm.csr unit 20
write cs(r) uv solute 1 unit 20
* cs(r) for CH31 into water with the charmm-prepared executable
close unit 20
open write name soluv1-charmm.gr unit 20
write g(r) uv solute 1 unit 20
* g(r) for CH31 into water with the charmm-prepared executable
close unit 20
open write name soluv1-charmm-plt2.gr unit 20
write g(r) uv solute 1 plt2 all from 0.5 thru 10.0 -
format(1x,10f10.5) unit 20
* g(r) for CH31 into tip3p water with the charmm-prepared executable
close unit 20
! calculate the chemical potential and the solute-solvent
! interaction energy. The cavity energy cannot be calculated
! bewcause we have not done the derivative calculation.
solvation chmpot energy plt2 verbose solute 1
! ===================================================================
! now do the second solute calculation
------------------------------------
iterate uv hnc solute 2 ncycle 500 nprint 1 -
init swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 2 hnc ncycle 500 nprint 1 -
swi(1) 0.01 swf(1) 0.1 dsw(1) 0.01 -
tol 0.9 rmix 0.39
iterate uv solute 2 hnc ncycle 5000 nprint 10 -
tol 0.001 rmix 0.39
! print out the solute-solvent g(r) characteristics
analysis uv solute 2
! write in files the distribution functions for the solute-solvent
! site pairs
open write name soluv2-charmm.csr unit 20
write cs(r) uv solute 2 unit 20
* cs(r) for CH31-CH32 into water with the charmm-prepared executable
close unit 20
open write name soluv2-charmm.gr unit 20
write g(r) uv solute 2 unit 20
* g(r) for CH31-CH32 into water with the charmm-prepared executable
close unit 20
open write name soluv2-charmm-plt2.gr unit 20
write g(r) uv solute 2 plt2 all from 0.5 thru 10.0 -
format(1x,10f10.5) unit 20
* g(r) for CH31-CH32 into tip3p water with the charmm-prepared executable
close unit 20
! calculate the chemical potential and the solute-solvent
! interaction energy
solvation chmpot energy plt2 verbose solute 2
! ===================================================================
! now do the solute 1 - solute 2 calculation
! store the potential of mean force in us(r)
iterate uu hnc w(r) solute 1 solute 2 ncycle 500 nprint 1 -
init tol 0.001 rmix 0.29
open write name sol1-sol2.pmf unit 20
write us(r) uu solute 1 solute 2 unit 20
* pmf for the solutes CH3E and CH31-CH32
close unit 20
open write name sol1-sol2.csr unit 20
write cs(r) uu solute 1 solute 2 unit 20
* cs(r) for the solutes CH3E and CH31-CH32
close unit 20
! ===================================================================
! now do the DERIVATIVE calculation
! test the calculation of the responce of the solvent to the
! solvation of a solute moleculte (infinite dilution)
! use tip3p water as solvent
! first for the solute 1
derivative hnc solute 1 ncycle 5000 nprint 1 -
init tol 0.001 rmix 0.39
open write name tip3p-uv1-charmm.dcsr unit 30
write dc(r) solute 1 unit 30
* derivative of cs(r) of tip3p upon solvation of CH31
close unit 30
open write name tip3p-uv1-charmm.dgr unit 30
write dg(r) solute 1 unit 30
* derivative of g(r) of tip3p upon solvation of CH31
close unit 30
! calculate the chemical potential, the interaction energy
! and the cavity formation energy
solvation chmpot energy cavity solute 1 verbose
! now do the calculation for solute 2
derivative hnc solute 2 ncycle 5000 nprint 1 -
init tol 0.001 rmix 0.39
open write name tip3p-uv2-charmm.dcsr unit 30
write dc(r) solute 2 unit 30
* derivative of cs(r) of tip3p upon solvation of CH31-CH32
close unit 30
open write name tip3p-uv2-charmm.dgr unit 30
write dg(r) solute 2 unit 30
* derivative of g(r) of tip3p upon solvation of CH31-CH32
close unit 30
! calculate the chemical potential, the interaction energy
! and the cavity formation energy
solvation chmpot energy cavity solute 2 verbose
!exit RISM
stop
!exit CHARMM
stop
----------------------------------------------------------------------