drude (c37b2)

New Drude Oscillator Format

by Benoit Roux (roux@uchicago.edu)
and Guillaume Lamoureux (Guillaume.Lamoureux@umontreal.ca)
and Edward Harder (eharder@uchicago.edu)
and Alex MacKerell Jr. (alex@outerbanks.umaryland.edu)

As of July 2007 the old "Drude Oscillator Command" and "ANISOTROPY
command" (see below) used to generate the Drude polarizable model will
be replaced by a new format that encodes the Drude model from the RTF.

In the present implementation the drude particles are
generated for all atoms for which polarizabilities (ie. via ALPHA) are
specified in the RTF file. This allows for the drudes to be generated
automatically when a molecule is generated in CHARMM. In addition,
code has been developed to allow for inclusion of atom-based Thole
scale factors, atom-based anisotropic polarizabilities and the
addition of lone pairs to selected atoms at the RTF level. These
enhancements allow for all the information for the polarizable drude
force field to be included in the RTF and parameter files.

For each atom with a specified polarizability, a "Drude oscillator"
is created by attaching to the atom an additional particle
(using a fictitious chemical bond of length zero and of force constant
'KDRUDE = k/2'). Each Drude particle is given a mass and a charge,
taken from the mass and the charge of its atom (so that the total mass
and charge are conserved for the "atom-Drude" pair).

As a whole, each "atom-Drude" pair has a charge 'Q', unchanged from
the partial charge the non-polarizable atom had prior to calling the
DRUDE command. The "atom-Drude" pair forms a dipole 'q*d', where 'q'
is the charge on the Drude particle and 'd' is the displacement vector
going from the atom to its Drude particle. Any external field 'E'
creates a net displacement 'd = q*E/k', and thus the "atom-Drude" pair
behaves as a point charge 'Q' with a polarizability 'alpha = q**2/k'.
The polarizabilities (in Angst**3) are read from WMAIN, and converted
into charges 'q', assuming a force constant 'k = 2*KDRUDE'.

See J. Chem. Phys. 119, 3025-3039 (2003) for more details.

In this implementation of the Drude oscillator, the force constant of the
spring is a diagonal rank-2 tensor with components KDRUDE. This leads to
an isotropic atomic polarizability, 'alpha = alpha_{11} = alpha_{22}
= alpha_{33} = q**2/k'. The ANISOTROPY command modifies the components of
the Drude force constant tensor allowing for anisotropic atomic
polarizabilites.

See J. Chem. Theory Comput. 2, 1587-1597 (2006) for more details.

The non-bonded lists are constructed such that, if the "real" atoms are
in a 1-2, 1-3, or 1-4 relationship, their corresponding Drude particles
will also be in a 1-2, 1-3, or 1-4 relationship, respectively.

The bonded interactions are modified to allow 1-2 and 1-3 screened
dipole-dipole interactions, as proposed by Thole [see Chem.Phys. 59,
341 (1981)]. If two atoms were not "seeing" each others in the
non-polarizable force field, their dipoles (and only their dipoles,
not their net partial charges) will "see" each others in the
polarizable force field. The screening function strength is modulated
by a parameter "a" that has been generalized to depend on the atom
type associated with the interacting pair of Drude oscillators
(i.e. a = a_i + a_j). These variable thole parameters "a_i" are
encoded in the RTF through the THOLE command.


* Description | Description of new DRUDE model RTF

Description of new DRUDE model RTF

1) Items in RTF file

A) The AUTOGENERATE command now includes a flag for the drude
particles. This should be specified at the beginning of the RTF.

AUTO ANGLES DIHE DRUDE

B) MASS statements must be included for Drude particle types.

MASS 104 DRUD 0.00000 DD ! drude particle

The default drude type is DRUD. However, alternate drude types may be
specified. These additional drude types must be i) specified with
MASS statements, ii) the ATOMs to which they are applied must include
a "TYPE drudetype" statement and iii) the NONBond parameters must be
specified. For example, to include a special drude type on water the
following would be needed in the RTF

i) MASS 153 DOH2 0.00000 DD ! water Drude
ii) ATOM OH2 ODW 0.00000 ALPHA -0.97825258 TYPE DOH2
iii) (NONBOND section) D* 0.0 -0.0000 0.0000
! Wildcard for Drudes and dummy atom
iv) (via NBFIX) MAGD DOH2 -0.01000 3.10000

Term iv) is an NBFIX that allows for the interactions between
magnesium and the water drude to be treated with a special LJ term.
Indeed, the motivation for additional drude types are such special
terms.

C) ALPHA and THOLE parameters are set in the RTF after the charge.
The presence of the "ALPHA" keyword flags that atom as being
polarizable and a drude particle is assigned to it upon generation of
the molecule. An atom based Thole scale factor may also be specified
via the "THOLE" keyword. If the THOLE term is missing, a default
value of 1.3 is assigned to that atom. This corresponds to a parameter
a = a_i + a_j = 2.6 which is the THOLE parameter in the old Drude
command syntax.

ATOM C C 0.630 ALPHA -1.104 THOLE 1.073

D) Specific drude types for a polarizable atom may be specified as
follows using the "TYPE" keyword. See 1A) above, sections i to iv for
more details.

ATOM C C 0.630 ALPHA -1.104 TYPE DC

E) Lone pairs may now be set in the RTF using a syntax similar to the
standard lonepair command » lonepair . All options for the
generation of lonepairs (FIXed, CENTer, COLOcate etc.) as specified
in the lonepair documentation may be used although the atom selection
specification is simplied as shown in the following example.

LONEPAIR relative LPA O C CL distance 0.3 angle 91.0 dihe 0.0
LONEPAIR relative LPB O C N distance 0.3 angle 91.0 dihe 0.0

F) Anisotropic atomic polarizabilities. Atom based anisotropic
polarizabilities may be assigned to selected atoms via the ANISOTROPY
syntax in the RTF. the first atom selects the atom on which the
polarizability is to be made anisotropic. The second atom along with
the first defines the "11" direction and the 3rd and 4th atom
selections define the "22" direction, with the anisotropy defined by
fractional polarizability components. Accordingly, only the 11 and 22
direction are needed since the trace of the A tensor is set to ONE. An
example follows

ANISOTROPY O C CL N A11 0.697 A22 1.219

2) Items in the Parameter file

A) The KDRUDE force constant for all the atoms is set by a wildcard in
the bond parameters. The term must be included for all drude types
included in the model. The wildcard terms can be overwritten by putting
chemical type specific bond paramters following the wild card term.

DRUD X 500.000 0.0000
DRUD O 487.740 0.0000

B) NONBOND parameters must be included for all drude types. In
addition, NBFIX terms for the drudes may be included as needed (see 1A
above).

C) Nonbond pair Thole screening interaction. The TCUT assign a radius within
all NB Thole interaction are counted. The 'aij' typically is assigned by the
user. A default value 1.2 can also be used.

THOLE TCUT 5.0 MAXNBTHOLE 50000
CL SODD @aij

3) Command Line Items

A) A "DRUDE" flag must included with the generate command to specify
the inclusion of drudes on the molecule. In addition, the drude mass
is also set in this command using the DMASS keyword followed by the
mass in AMU. The default value for the drude mass is XXXX.

generate NMA first none last none setup warn DRUDE DMASS 0.4


Description of Extended PSF format for CHARMM and NAMD


New extended format PSF is designed for Drude model. The default format is
for CHARMM and xplor format is for NAMD. The PSF explicitly provides Thole,
Polarizability, lone pair and anisotropic information for CHARMM/NAMD PSF reader.
Generation of Drude models based on nonpolarizable model is also extended to
polypeptides and proteins (including generation of disu bond and patch).


Drude Oscillator Command


by Benoit Roux (Benoit.Roux@med.cornell.edu)
and Guillaume Lamoureux (Guillaume.Lamoureux@umontreal.ca)

The DRUDE command generates a polarizable system by modifying the
topology and parameters of an existing non-polarizable system. For
each selected atom, it creates a "Drude oscillator" by attaching to
the atom an additional particle (using a fictitious chemical bond of
length zero and of force constant 'KDRUDE = k/2'). Each Drude
particle is given a mass and a charge, taken from the mass and the
charge of its atom (so that the total mass and charge are conserved
for the "atom-Drude" pair).

As a whole, each "atom-Drude" pair has a charge 'Q', unchanged from
the partial charge the non-polarizable atom had prior to calling the
DRUDE command. The "atom-Drude" pair forms a dipole 'q*d', where 'q'
is the charge on the Drude particle and 'd' is the displacement vector
going from the atom to its Drude particle. Any external field 'E'
creates a net displacement 'd = q*E/k', and thus the "atom-Drude" pair
behaves as a point charge 'Q' with a polarizability 'alpha = q**2/k'.
The polarizabilities (in Angst**3) are read from WMAIN, and converted
into charges 'q', assuming a force constant 'k = 2*KDRUDE'.

See J. Chem. Phys. 119, 3025-3039 (2003) for more details.

The bonded lists are modified so that, if the "real" atoms are in a
1-2, 1-3, or 1-4 relationship, their corresponding Drude particles
will also be in a 1-2, 1-3, or 1-4 relationship, respectively. (This
is done by creating additional fictitious bonds of force constant zero
between the particles.)

For a single atom (charges in parenthesis):

DRUDE (q)
A --------> A~DA
(Q) (Q-q)

For a diatomic molecule:

A1 DRUDE A1~DA1
| --------> |
A2 A2~DA2

1-2 pairs: A1-A2, A1-DA2, DA1-A2, DA1-DA2

For a triatomic molecule:

A1 A1~DA1
\ DRUDE \
A2 --------> A2~DA2
/ /
A3 A3~DA3

1-2 pairs: A1-A2, A1-DA2, DA1-A2, DA1-DA2,
A2-A3, A2-DA3, DA2-A3, DA2-DA3
1-3 pairs: A1-A3, A1-DA3, DA1-A3, DA1-DA3

The bonded interactions are modified to allow 1-2 and 1-3 screened
dipole-dipole interactions, as proposed by Thole [see Chem.Phys. 59,
341 (1981)]. If two atoms were not "seeing" each others in the
non-polarizable force field, their dipoles (and only their dipoles,
not their net partial charges) will "see" each others in the
polarizable force field.

In this implementation of the Drude oscillator, the force constant of the
spring is a diagonal rank-2 tensor with components KDRUDE. This leads to
an isotropic atomic polarizability, 'alpha = alpha_{11} = alpha_{22}
= alpha_{33} = q**2/k'. The ANISOTROPY command modifies the components of
the Drude force constant tensor allowing for anisotropic atomic
polarizabilites.


* Syntax | Syntax of the DRUDE command
* Description | Description of the DRUDE command
* Toppar | Effect on the topology and parameters
* Warnings | To be aware of when using the DRUDE command
* Examples | Usage examples of the DRUDE command


Top
Syntax of the DRUDE command


DRUDe RESEt

DRUDe [MASS real] [KDRUde real] -
[VTHOle logical] [THOLe real [SHAPe integer]] -
atom-selection


atom-selection::= (» select .)


Top
Description of the DRUDE command


-------------------------------------------------------------------
Keyword Default Purpose
-------------------------------------------------------------------
RESET Desactivates the Drude particles. After a reset,
the user should delete all Drude particles.

MASS 0.0 Mass of the Drude oscillators (in amu). The
default zero value causes the masses to be read
from the topology file. Any nonzero value will
override the topology file.

KDRUDE 0.0 Force constant of the atom-Drude bonds
(in kcal/mol/Angst**2). The default zero value
causes the bond force constants to be read from
the parameter file. Any nonzero value will
override the parameter file.

VTHOLE Uses variable thole parameters for dipole-dipole
interactions.

THOLE 2.6 The screening factor for dipole-dipole interactions
between atoms excluded from the non-bonded
interactions. To have no dipole-dipole
interactions between these bonded atoms, use
THOLE = 0.

SHAPE 1 Specifies the shape of the dipole-dipole
screening function.


-------------------------------------------------------------------
1) KDRUDE

KDRUDE is the force constant (in kcal/mol/Angst**2) for the bond
between each atom and its Drude particle the user wishes to use. It
is overriding any bond constant found in the parameter file. For
highly polar molecules like water, the recommended value for KDRUDE is
500 kcal/mol/Angst**2.

The atomic polarizabilities (in Angst**3) are read from the WMAIN
array:
alpha = abs(WMAIN)

The charge on every Drude particle is computed using the following
formula:
q = sqrt( 2*KDRUDE * alpha / CCELEC ) * sign(WMAIN)

The charges are given the signs of the WMAIN values. As long as
KDRUDE is large enough, the Drude particles will stay very close to
their atoms, and the sign of 'q' is irrelevant.


-------------------------------------------------------------------
2) THOLE, SHAPE

(For 1-2 and 1-3 atoms only. All other interactions are regular
Coulomb.)

The THOLE parameter is a dimensionless factor that specifies the
extent of the smearing of the charge 'q' on the Drude oscillators and
of a contribution '-q' on the "real" atom. The default value of THOLE
is 2.6, that is, the 1-2 and 1-3 dipole-dipole interactions are turned
on by default. To turn the interactions off, set THOLE to zero.

The default constant THOLE of 2.6 can be replaced by variable thole
parameters using the VTHOLE keyword on the DRUDE command line.
The THOLE parameter between oscillators I and J is given by
THOLE = THOLEI + THOLEJ. The THOLEI parameters for each atom are fit
along with the charges against ab initio data. Values of THOLEI must
be given in the WCOMP array for all Drude oscillator containing atoms
prior to the DRUDE command.

Because the dipole are explicitly made of two charges, the screened
dipole-dipole interaction between two polarizable atoms (that is, two
"atom-Drude" pairs) is actually the sum of the following four screened
charge-charge interactions:
('q1' on Drude 1) - ('q2' on Drude 2)
('q1' on Drude 1) - ('-q2' on atom 2)
('-q1' on atom 1) - ('q2' on Drude 2)
('-q1' on atom 1) - ('-q2' on atom 2)

The screened charge-charge interaction has the form:
U(r12) = CCELEC * q1*q2 * S(u12)/r12
where 'u12' is the normalized distance:
u12 = r12 * THOLE / (alpha1*alpha2)**(1/6)

'S' is a screening function defined by the SHAPE parameter:

SHAPE Screening function Charge distributions
1 S(u) = 1 - (1+u/2)*exp(-u) Slater-Delta
2 S(u) = erf(u) Gaussian

The default value of SHAPE is 1, which is also the only shape
currently implemented. SHAPE=2 is reserved for Gaussian-Gaussian
distributions.

Two "atom-Drude" pairs have dipole-dipole interactions if the
following conditions are met:
1. The THOLE parameter is nonzero.
2. In the non-polarizable force field, the two atoms where
in the nonbonded exclusion list.

To see if all the desired atoms have dipole-dipole interactions, use
PRNLEV > 7. Each call to the energy will print the atom numbers,
polarizabilities and Drude particles's charges of each interacting
pair.

The energy from the dipole-dipole interactions is added to the ELEC
energy term, and "SKIP ELEC" will skip the Thole interactions as well.


Top
Effect on the topology and parameters


-------------------------------------------------------------------
1) New atoms

The Drude particles are inserted immediately after their corresponding
atoms. For an atom type 'CA1', the DRUDE command will assign the atom
type 'DCA1' for the Drude particle. Since no regular atoms have names
starting with a 'D', the Drude oscillators can be selected with
"SELECT TYPE D* END".


-------------------------------------------------------------------
2) Masses

The masses for the selected atoms are modified so that the total mass
of the atom-Drude pair corresponds to the atomic mass. Try "SCALAR
MASS SHOW" before and after calling the DRUDE command.


-------------------------------------------------------------------
3) Charges

The charges for the selected atoms are modified so that the total
charge of the atom-Drude pair corresponds to the atomic partial
charge. Try "SCALAR CHARGE SHOW" before and after calling the DRUDE
command.


-------------------------------------------------------------------
4) Bonded interactions

In addition to the atom-Drude bonds, zero force bonds are created to
maintain between the atom-Drude pairs the same 1-2, 1-3, and 1-4
relationships that were existing previously to the DRUDE call. For
two bonded atoms A1 and A2, with Drude particles DA1 and DA2

DA1 DA2
| |
A1 ----- A2

zero force bonds are created between DA1 and DA2, between DA1 and A2,
and between A1 and DA2, so that any particle of the A1-DA1 pair is 1-2
bonded to any particle of the A2-DA2 pair. Since the force constants
of these fictitious bonds are zero, the computational overhead is
minimal.


-------------------------------------------------------------------
5) Non-bonded interactions

Weither the Drude particles have Lennard-Jones parameters or not, the
Lennard-Jones parameters of the selected atoms are kept unchanged.
Since the polarizable force field is built from the same "ingredients"
as the non-polarizable force field, all the NBONDS options can be used
as before (notably the PMEWALD method).


Top
To be aware of when using the DRUDE command


-------------------------------------------------------------------
1) Call the DRUDE command after all the atoms are built

Otherwise, some zero-force bonds between the Drude particles and
neighboring atoms (as discussed in the previous section) may be
missing. And since bad contacts are difficult to resolve with a
polarizable force field, it is probably safer to minimize/equilibrate
the system using first a non-polarizable force field.


-------------------------------------------------------------------
2) Call the DRUDE command before SHAKE and LONEPAIR

The preferred call to SHAKE is:

COOR COPY COMP
SHAKE BONH PARAM TOLERANCE 10E-9 -
NOFAST -
SELECT .NOT. TYPE D* END -
SELECT .NOT. TYPE D* END


-------------------------------------------------------------------
2) Always delete all the Drude particles after a RESET

Treat this sequence of commands a single command:

DRUDE RESET
DELETE ATOMS SELECT TYPE D* END

The "DRUDE RESET" command puts back the mass and the charge of the
Drude particles on the heavy atoms, and erases the distinction between
a Drude particle and a regular atom.


-------------------------------------------------------------------
3) Beware of atom names conflicts

Since the atom names don't have more than four letters, atoms with
different names may end up having Drude particles with the same
name:

C210 --> DC21
C211 --> DC21


-------------------------------------------------------------------
4) MASS and KDRUDE are overriding the toppar files

Any nonzero value for MASS and KDRUDE specified by the user is
overriding the values from the topology and parameter files.


Top
Usage examples of the DRUDE command


-------------------------------------------------------------------
1) Polarizable benzene
(see test/c30test/drude_benzene.inp)

After reading the standard, non-polarizable topology and parameter
files, a standard benzene molecule is generated:

READ SEQUENCE BENZ 1
GENERATE BENZ SETUP FIRST NONE LAST NONE

The polarizabilities on all carbon atoms are set to 1.5 Angst**3:

SCALAR WMAIN SET +1.5 SELECT .NOT. TYPE H* END
DRUDE SELECT .NOT. TYPE H* END

The selection contains the atoms CG, CD1, CD2, CE1, CE2, and CZ. The
DRUDE command will look for atom types DCG, DCD1, DCD2, DCE1, DCE2,
and DCZ. If these types are unknown, the program will crash. For
this reason, it is necessary to append the atom types of the Drude
particles when reading the topology:

OPEN READ CARD UNIT 1 NAME @TOPPAR/top_all22_drude.inp
READ RTF CARD APPEND UNIT 1

Similarly, the program will crash if bond parameters are missing, and
the additional bond parameters should be appended to the parameters:

OPEN READ CARD UNIT 1 NAME @TOPPAR/par_all22_drude.inp
READ PARAM CARD APPEND UNIT 1

The structure is minimized:

MINI SD STEP 0.001 NSTEP 1000 NPRINT 100

Since benzene is a nonpolar molecule, the Drude particles are not
significantly moved from their heavy atoms. To find the induced
atomic dipoles for a given structure, one should use "CONS FIX SELECT
.NOT. TYPE D* END" before calling MINI.

The molecular polarizability is obtained using the VIBRAN command with
the DIPOLES keyword:

VIBRAN
DIAGONALIZE
PRINT NORMAL VECTORS DIPOLES SELECT ALL END
END

The total polarizability is an anisotropic tensor similar to the
experimental results for benzene [J.Chem.Phys. 95, 5873 (1991)]. The
strong anisotropy comes from the 1-2 and 1-3 dipole-dipole
interactions. Desactivating these interactions by using THOLE=0, the
polarizability tensor is almost isotropic.


-------------------------------------------------------------------
2) SWM4-DP water
(see test/c30test/swm4.inp)

See J. Chem. Phys. 119, 5185-5197 (2003) and Chem. Phys. Lett. 418,
245-249 (2005) for a complete description of the model.
After reading the topology and parameter files, the model is built as
following:

READ SEQUENCE SWM4 ...
GENERATE WAT SETUP NOANGLE NODIHEDRAL

READ COOR CARD ...

SET ALPHAO = 1.042520
SET DOM = 0.238080

SCALAR WMAIN SET @ALPHAO SELECT ( SEGID WAT .AND. TYPE OH2 ) END
DRUDE SELECT ( SEGID WAT .AND. TYPE OH2 ) END

COOR COPY COMP
SHAKE BONH PARAM TOLERANCE 1.0E-9 -
NOFAST -
SELECT ( SEGID WAT .AND. .NOT. TYPE D* ) END -
SELECT ( SEGID WAT .AND. .NOT. TYPE D* ) END

LONEPAIR BISECTOR DIST @DOM ANGLE 0.0 DIHE 0.0 -
SELECT ATOM WAT * OM END SELECT ATOM WAT * OH2 END -
SELECT ATOM WAT * H1 END SELECT ATOM WAT * H2 END


The molecular dynamics for polarizable water is explained in
» vv2 .


ANISOTROPY Command


by Edward Harder (eharder@uchicago.edu)
and Benoit Roux (roux@uchicago.edu)

In the above implementation of the Drude oscillator, the force constant
of the spring is a diagonal rank-2 tensor with components KDRUDE. This
leads to an isotropic atomic polarizability, 'alpha = alpha_{11} =
alpha_{22} = alpha_{33} = q**2/k'. The ANISOTROPY command modifies the
components of the Drude force constant tensor allowing for anisotropic
atomic polarizabilites.


* Syntax | Syntax of the ANISOTROPY command
* Description | Description of the ANISOTROPY command
* Toppar | Effect on the topology and parameters
* Warnings | To be aware of when using the ANISOTROPY command
* Examples | Usage examples of the ANISOTROPY command

Syntax of the ANISOTROPY command


ANISOTROPY [MASS real] [KDRUde real] -
[THOLe real [SHAPe integer]] -
atom-selection


atom-selection::= (» select .)

Description of the ANISOTROPY command


-------------------------------------------------------------------
Keyword Default Purpose
-------------------------------------------------------------------
K11, KDRUDE Components of the force constant tensor
K22, (in kcal/mol/Angst**2). The default value
K33, is the KDRUDE parameter assigned from the DRUDE
command.

VERBOSE Prints atoms involved in selection and
components of the force constant tensor.

-------------------------------------------------------------------

1) K11, K22, K33

K11, K22, K33 are the components of the force constant tensor
(in kcal/mol/Angst**2). The directions 1, 2 and 3 are defined in the
molecular reference frame using atom selections that follow the
assignment of these variables. The first atom selection contains the
anisotropic Drude oscillator. The vector connecting the first atom to
the second atom selection defines the 1 direction. The vector between
the 3rd and 4th atom selections defines the 2 direction. The 3 direction
is orthogonal to 1 and 2. The charge on the Drude for anisotropic
oscillators is:

q = sqrt( 2*K33 * alpha / CCELEC ) * sign(WMAIN)


To be aware of when using the ANISOTROPY command


-------------------------------------------------------------------
1) Call the ANISOTROPY command after the rest of the charge model
has been built (i.e. DRUDE and LONEPAIR)

Otherwise, inconsitencies in the particle charges and intended
polarizabilites may result.

Usage examples of the ANISOTROPY command


-------------------------------------------------------------------
1) Polarizable NMA


ANISOTROPY -
K11 700 K22 400 K33 450 select segid NMA .and. type O show end -
select segid NMA .and. type C show end -
select segid NMA .and. type CL show end -
select segid NMA .and. type N show end VERBOSE

The atomic polarizability of the carbonyl oxygen in NMA is made
anisotropic. The 1 direction is parallel to the carbonyl bond.
The 2 direction is parallel to the vector between the CL carbon
and nitrogen. The 3 direction is normal to the plane spanned by
1 and 2.


Syntax of the DrudeHardWall command

DrudeHardWall L_WALL real

Example:

DrudeHardWall L_WALL 0.2
! set the hard wall at 0.2 Angstrom

DrudeHardWall L_WALL 0.0
! turn off the hard wall when L_WALL equals 0.0

Description of the DrudeHardWall command
When drudes go too far away from nucleus, simulations could be very
unstable. Introducing hard wall constraints on the length of drude
bonds is a possible way to avoid such instability. In each MD step,
the length of drude bonds are checked and compared with "L_WALL".
When the length of drude bond is larger than "L_WALL", the relative
velocities along bond vector are flipped and scaled down according to
the temperature of drude bond. The displacement relative to "L_WALL"
is flipped and scaled down according to new velocities along bond
vector to make sure drude bond is not longer than "L_WALL".