Partial atomic charges and their impact on the free energy of solvation

Partial Atomic Charges and Their Impact on the FreeEnergy of Solvation

Joakim P. M. J€ambeck,*[a] Francesca Mocci,[a,b] Alexander P. Lyubartsev,[a]

and Aatto Laaksonen[a,b]

Free energies of solvation (DG) in water and n-octanol have

been computed for common drug molecules by molecular

dynamics simulations with an additive fixed-charge force field.

The impact of the electrostatic interactions was investigated

by computing the partial atomic charges with four methods

that all fit the charges from the quantum mechanically

determined electrostatic potential (ESP). Due to the

redistribution of electron density that occurs when molecules

are transferred from gas phase to condensed phase, the

polarization impact was also investigated. By computing the

partial atomic charges with the solutes placed in a conductor-

like continuum, the charges were effectively polarized to take

the polarization effects into account. No polarization

correction term or similar was considered, only the partial

atomic charges. Results show that free energies are very

sensitive to the choice of atomic charges and that DG can

differ by several kBT depending on the charge computing

method. Inclusion of polarization effects makes the solutes too

hydrophilic with most methods and in vacuo charges make

the solutes too hydrophobic. The restrained-ESP methods

together with effectively polarized charges perform well in our

test set and also when applied to a larger set of molecules.

The effect of water models is also highlighted and shows that

the conclusions drawn are valid for different three-point

models. Partitioning between an aqueous and a hydrophobic

phase is also described better if the two environment’s

polarization is taken into account, but again the results are

sensitive to the charge calculation method. Overall, the results

presented here show that effectively polarized charges can

improve the description of solvating a drug-like molecule in a

solvent and that the choice of partial atomic charges is crucial

to ensure that molecular simulations produce reliable results.

VC 2012 Wiley Periodicals, Inc.

DOI: 10.1002/jcc.23117

Introduction

Few would argue against that the free energy is one of the

most important concepts in thermodynamics. Changes in the

free energy control how small drug molecules are dissolved in

water and how biologically active they are in terms of ligand

binding and cell penetration. The knowledge of the free

energy is therefore of great interest in rational drug design[1,2]

and as a result of this, a great deal of effort has been put into

developing methods and algorithms that can compute this

property in an accurate and efficient fashion. With the increase

in available computing power, the aspects of these calcula-

tions that were once looked on as highly computationally in-

tensive tasks, due to the prerequisite to sample, every ther-

mally available part of phase space, are beginning to fade

away. As this is true for the free energy of solvation of smaller

molecules, the problem of predicting ligand binding affinities

in a more efficient and systematic manner still remains.[1,3] In

some thermodynamic cycles, the free energy of hydration

(DGhyd) has to be determined accurately to predict ligand

binding affinities.[4] Further, DGhyd is important for drugs’ solu-

bility[5] and their partitioning between between phases, usually

water and n-octanol are used in experimental studies of drug

cell permeation. The latter is often used as a model of the cell

membrane in experimental studies with so-called log P val-

ues.[6,7] Therefore, hydration free energies play a central role in

our molecular understanding of several important processes.

Computations of free energies of solvation also give impor-

tance guidelines on which level of accuracy that should be

expected in other applications as well act as a fundamental

test of force fields (FFs).

Usually, an empirical energy function, called FF, is used to

describe the intermolecular and intramolecular interactions in

a system composed of solvent and solute(s), that is, a model

Hamiltonian. Molecular dynamics (MD) or Monte Carlo (MC)

algorithms are then used to sample the different configura-

tions of the system[8] and free energies can then be computed

with the aid of statistical mechanics. Different methods can be

applied to obtain free energies from these sampling proce-

dures: thermodynamic integration[9] that has been used in a

number of studies,[10–12] the Bennett acceptance ratio

method,[13–16] free energy perturbation,[17–19] or the expanded

ensemble (EE) method.[20–23] The mentioned studies are just a

handful of the recent published work as it would be an over-

whelming task to go through the whole field. The major

[a] J. M. J€ambeck, F. Mocci, A. P. Lyubartsev, A. Laaksonen

Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University,

Stockholm, SE-10691, Sweden

E-mail: [email protected] or [email protected]

[b] F. Mocci, A. Laaksonen

Department of Chemical and Geological Sciences, University of Cagliari, Italy

Contract/grant sponsor: Swedish Research Council (VR).

VC 2012 Wiley Periodicals, Inc.

Journal of Computational Chemistry 2013, 34, 187–197 187

FULL PAPERWWW.C-CHEM.ORG

http://onlinelibrary.wiley.com/

difference between the EE method and the other mentioned

methods is the way the simulations are set up. In order for

any free energy computation to be efficient, an ensemble of

intermediate states has to be assigned between the reference

state and the target state to secure a significant phase space

overlap. This results in a large number of simulations that have

to be performed and also requires a lot of postsimulation anal-

ysis to ensure proper overlap of states and so on. Therefore,

these procedures are very time-consuming and do not always

guarantee a precise value of the free energy.[10] Due to the

large throughput in drug design, it is desirable to have an effi-

cient methodology. With the EE method (described in more

detail later), the sampling of the phase space is governed by

random walk over the reference, a number of intermediate

and target states. As this is done in an automated fashion, it is

possible to obtain the free energy of solvation in one single

MD simulation which makes this procedure very efficient. The

EE method has been used in many studies to compute free

energies.[23–31]

It is important to point out that merely choosing an effec-

tive way of obtaining the free energy of solvation from simula-

tions is not enough. There are other vital choices one has to

make and perhaps the most crucial one is the FF. The set of

parameters in the FF that has the largest impact on the

computation of free energies are the partial atomic

charges[14,18,18,32,33] (if the discussion is limited to point charge,

additive FFs). Although atomic charges are determined by

quantum mechanical (QM) based calculations for FFs like

AMBER and to a lesser extent CHARMM, they have an inherent

problem—atomic charges are not QM observables, that is,

there is no strict physical definition of them. Electrostatic

moments such as dipole, quadrupole, and so forth can be

measured in laboratories and give (limited) information regard-

ing the charge distribution but for larger molecules this

becomes cumbersome. As there is no unambiguous way of

determining these partial atomic charges, a number of meth-

ods have been developed. One method of obtaining atomic

charges is by minimizing the difference between the electro-

static potential (ESP) determined from the wave function and

the ESP created by the point charges.[34] With this procedure,

the spherically symmetric point charges of each atom in the

molecule reproduce the ESP as well possible. As the ESP is a

QM observable, this is a straightforward procedure with a

more physical foundation than for instance Mulliken charges.

A problem that arises with this approach is how one should

sample the QM ESP. Several schemes have been suggested:

CHELP,[35] CHELPG,[36] and the Merz-Singh-Kollman (MK)

scheme.[34,37] All the mentioned methods sample the ESP at a

number of points outside the van der Waals (vdW) radii of the

constituting atoms of the molecule. The CHELP scheme uses

points at a distance of 2.5, 3.5, 4.5, 5.5, and 6.5 A from the

vdW surface, CHELPG samples the ESP at points evenly distri-

buted between 0 and 2.8 A from the vdW surface and the MK

scheme at shells at a distance of 1.4, 1.6, 1.8, and 2.0 times

the vdW radii. One inherent problem with all the mentioned

methods is the determination of the ESP ‘‘belonging’’ to the

more buried atoms such as sp3-hybridized carbons.[38,39] Fur-

ther, there is a pronounced conformational dependency of the

charges[40–42] which in turn will affects the computed free

energy of solvation.[43–45] One way of addressing the problem

with the charges of buried atoms and to temper the confor-

mational dependency is to use the restrained-ESP (RESP)[46]

approach. With this method, a hyperbolic penalty function is

used to restrain the charges to keep their magnitudes down,

and the ESP can be sampled with any of the three earlier

mentioned methods.

There are two problems with all the approaches described

above, namely the assumption that the charge density is sym-

metric around the atoms and the lack of polarization. Both

issues are inherent problems of additive FFs which requires a

lot of effort to correct. Still classical, point-charge FFs are used

due to their surprising accuracy and modest time cost com-

pared to, for example, polarizable FFs. The lack of polarization

is of great importance as for polar molecules, the charge distri-

bution can change considerably when transferring the mole-

cule from gas phase to condensed phase.[47,48] Water for

instance induces a strong electric field which polarizes the sol-

ute(s). Often charge calculations are performed with the solute

in gas phase where this redistribution of charges is ignored.

The effects of neglecting the polarization have been noted

previously in the literature.[23,49] One straightforward way to

include polarization effects would be to perform the QM calcu-

lations with a self-consistent reaction field. By doing so, the

ESP obtained would be polarized and therefore the partial

charges derived from this ESP would be effectively polarized

when used in simulations of condensed phase systems. This

solution has been proposed before[23] and has also been

applied.[14,49–51] Here, we further test if this method improves

the free energy calculations by systematically computing free

energies of solvation for a variety of molecules containing

functional groups of different nature. The aim is to identify the

scheme that results in the most reliable free energies of solva-

tion. Due to the freedom in how to sample the ESP, we here

systematically compare the results in terms of free energy of

solvation for 13 typical drug compounds for which the atomic

charges were computed with the four earlier mentioned

methods, with and without effectively polarized charges. This

resulted in 104 computed DGhyd values. To test the procedure

for a solvent with a smaller dielectric constant, the same types

of calculations were performed in n-octanol (from now on

referred to as octanol). This makes it possible to compute

log P values which are of great interest in drug design. In

total, 367 free energies of solvation and 104 log P values were

computed and compared to experiments when allowed.

Methodology

Modeling of solutes and solvents

Thirteen well-known drug molecules were chosen for compu-

tation of free energies of solvation (Figure 1). FF parameters

for the solute and octanol were taken from GAFF[52] as this FF

has proven to give reliable results in a number of free energy

studies.[14–16,30,31] Charges for octanol were taken from a

FULL PAPER WWW.C-CHEM.ORG

188 Journal of Computational Chemistry 2013, 34, 187–197 WWW.CHEMISTRYVIEWS.COM

previous investigation[23] and this set of charges was used

throughout the whole of this investigation. Partial charges for

the solutes were determined by first optimizing the geometry

of the solutes in vacuum at a DFT level of theory with the

B3LYP exchange-correlation functional[53–56] with the 6-

311þG(d,p) basis set. Frequency analysis was conducted to

verify the nature of the stationary points found. Polarization

effects were modeled by performing single-point calculations

on the optimized geometries with the conductor-like contin-

uum model[57,58] for two solvents, water (e ¼ 78.4) and octanol

(e ¼ 9.86). Once self-consistency was obtained, the polarized

ESPs were used for charge fitting. Four methods were used for

obtaining the partial charges: CHELP, CHELPG, MK, and RESP.

For the latter, the ESP was sampled with the MK scheme. Also,

charges from vacuum calculations were computed with all ESP

methods to see the impact of the effectively polarized charges.

All QM calculations were performed with the Gaussian09 pro-

gram suite[59] and the RESP fittings were done with the Red

program developed by Dupradeau et al.[60] Default parameters

for all calculations in Gaussian09 were used. The ESPs were

sampled at the same level of theory as the geometry optimiza-

tions were performed at, since it has been established that the

B3LYP functional gives reliable charges,[61,62] especially if used

with a basis set including polarized functions.[63] It should be

mentioned that the free energies reported here do not include

the energetic cost that comes with changing a molecule’s

in vacuo equilibrium electron distribution when transferring it

to condensed phase although there have been methods pur-

posed for this.[11,47–49] To simulate water, the flexible SPC

(fSPC) model by Toukan and Rahman[64] was chosen. The fSPC

water molecule is able to slightly change its geometry in

response to its environment and has proven to reproduce the

experimental dielectric constant for bulk water[65] which is of

great importance for solvation studies. Additional simulations

have been carried out with SPC/E[66] and TIP3P[67] water mod-

els as well.

Computation of free energies

In this work, we implemented some modifications of the origi-

nal EE method[20,21] which are briefly described below. The EE

method implies a gradual insertion/deletion of the studied sol-

ute molecule into/from the solvent. The insertion parameter ais introduced which describes the degree of insertion of the

solute, so that a ¼ 1 describes solute molecule fully interact-

ing with the solvent while a ¼ 0 represents the solute com-

pletely decoupled from the solvent (that is, case a ¼ 0

describes pure solvent and the solute molecule in a gas phase

of the same volume). The insertion parameter can accept a

number of (fixed) values {ai},i ¼ 0,…, M in the range between

0 and 1. During the simulation, which can be carried out by ei-

ther MC[20] or MD[21] algorithms, attempts are made to change

the insertion parameter to another (normally, neighboring)

value, with acceptance probability

Pði ! i61Þ ¼ min 1; exp � VSsðai61Þ � VSsðaiÞ � ðgi61 � giÞkBT

� ��

ð1Þ

where VSs(ai) is the interaction energy of the solute particle

with the solvent corresponding to the given insertion parame-

ter ai and gi are so-called balancing (weighting) factors intro-

duced with the purpose to make distribution over subensem-

bles close enough to the uniform one. During the simulation,

Figure 1. Molecules for which free energies of solvation in water and n-octanol were calculated.




probabilities of different subensembles qi are defined, and free

energy difference between states with fully inserted and fully

deleted solute (excess solvation free energy) is computed by

DG ¼ �kBT lnqMq0

þ gM � g0 (2)

In previous works on computation of the solvation free

energies,[23,68] a linear scaling of solute–solvent interaction

with a was used, namely VSs(a) ¼ aVSs(1). Such a scheme has a

shortage that the repulsive core of the Lennard-Jones (LJ)

potential decreases very slowly with decrease of a, which leads

to necessity to consider very small a values. Now, we scale

interaction VSs between the solute and solvent atoms (which is

supposed to be a sum of the LJ and electrostatic terms)

according to the following:

VSsðaÞ ¼ a4VSsLJ ð1Þ þ a2VSs

el ð1Þ (3)

The rationale between a4 scaling of the LJ interaction is that

the effective core radius of the LJ potential scales then as

(a4)1/12 ¼ a1/3, and thus the effective volume of the core

(approximately proportional to the free energy of cavity forma-

tion) scales linearly with a. Scaling a2 for the electrostatic inter-

actions is chosen to switch off them faster than the repulsive

LJ interaction, to minimize problems with hydrogen atoms of

water molecules which do not have LJ potential. With scaling

of the solute–solvent interaction, described by eq. 3, it is pos-

sible to choose ai points uniformly distributed in the range

[0:1], so that reasonable acceptance probability of transitions

is maintained through the whole range of subensembles. In

the Supporting Information, this approach is validated.

Another modification of the EE procedure implemented in

this work is the automatic choice of the balancing factors giby the Wang-Landau algorithm.[69] This algorithm is typically

used for equilibration of weights in the multicanonic[70] or

entropic sampling[71] simulations. In application to the EE

technique, the Wang-Landau algorithm can be reformulated as

described below. We start simulations with zero balancing fac-

tors. After visiting a subensemble, a small increment Dgi is

subtracted from the corresponding value of the balancing fac-

tor, which decreases the probability to go to already visited

states and favors to attaining a uniform distribution. After a

certain number of steps (a sweep), when the system visited all

subensembles and passed several times between the end

points, the value of the increment is decreased twice. After a

certain number of sweeps (usually 10-12), the value of the in-

crement becomes very small, and simultaneously the profile of

balancing factors is tuned in a way providing uniform walking

in the space of subensembles. After that the equilibration

stage ends, production run with fixed balancing factors is

made yielding the solvation free energies.

Simulation details

All MD simulations were performed in the isobaric–isothermal

ensemble, NPT, where the temperature was kept constant

at 310 K and the pressure at 1 atmosphere with the

Nos�e-Hoover[72,73] thermostat (with relaxation time 30 fs) and

barostat (relaxation time 1 ps), respectively. Periodic boundary

conditions were used in every dimension. Aqueous simulation

boxes contained 500 fSPC water molecules and one solute

that was gradually inserted. Octanol simulations were per-

formed with 125 octanol molecules and 46 fSPC water mole-

cules, which corresponds to the experimental molar ratio of a

saturated octanol/water solution. Note that saturation ratio of

the considered models may differ from the experimental one.

At start, the molecules were placed in the simulation box in a

regular fashion with the centers of mass at a FCC lattice, and

restriction for absolute value for forces between the atoms

was used to smoothly remove initial overlapping contacts. The

cutoff value for forces was set at the level which is never

reached in the equilibrated system. The systems were relaxed

in a 100 ps long simulation in the canonical ensemble (NVT)

followed by a 2 ns long equilibration in the NPT ensemble.

Production runs were run for 20 ns where for the first 10 ns,

the balancing factors used in the EE scheme were equilibrated

and the remaining 10 ns were used for actually computing the

free energy of solvation. In simulations with fSPC water as well

as in octanol simulations, the double time-step method of

Tuckerman et al.[74] was used with a 0.2 fs short time step for

faster molecular motion (internal motion) and a longer time

step of 2.0 fs for the slower molecular motions. For simulations

with rigid TIP3P and SPC/E water model, the bonds were con-

strained using SHAKE algorithm with tolerance 0.0001, and

leap-frog algorithm with time step 2 fs was used. LJ forces

were computed up to a distance of 0.5 nm for the short time

step and rcut ¼ 1.2 nm for the longer time step and the neigh-

bor list was updated every 10 steps. Electrostatic interactions

were treated by the Ewald summation method with the real-

space Ewald factor 2.8/rcut and cutoff in the reciprocal space

was set from the condition that the remaining terms do not

contribute by more than 0.0001 level of the total value. The

long-range dispersion corrections to the energy and pressure

were included. Between 25 and 40 subensembles, with uni-

formly distributed a values, were used in the calculations

depending on the solute size, which provided overall accep-

tance ratio of 30–35% for transitions between the subensem-

bles. All errors reported were computed via block averaging

over the production runs with blocks of 1 ns (excluding the

initial 10 ns were the balancing factors are equilibrated). The

EEMD calculations were performed by MDynaMix v. 5.2.4 pack-

age[75] (available from www.mmk.su.se/mdynamix).

Results and Discussion

Free energies of hydration

In Table 1, the free energies of hydration are shown together

with available experimental data. The spread of DGhyd is strik-

ing and shows how sensitive these types of calculations (and

in general molecular simulations with FFs) are. Previously, the

impact of partial atomic charges has been pointed out in free

energy calculations[14,18,23,33] but not to the same extent as

reported here. The present investigation includes molecules of



very polar nature, which could be a reason for this very pro-

nounced dependency. When polarization effects are included,

all methods systematically underestimate DGhyd with the

exception of RESP. The partial atomic charges obtained in cal-

culations where polarization was taken into account appear to

be overpolarized. It is clear that the RESP charges do this to

the smallest extent and MK to the largest, and this is to be

expected as it has previously been shown that the MK scheme

gives charges of larger magnitude when compared with other

methods.[61,76] Actually, every free energy of hydration is

underestimated by the MK charges. In Figure 2, the correlation

between experiments and simulations are shown and as can

be seen, the underestimation is very evident. Further, in the

case of the polarized charges, it is clear that MK and CHELPG

give similar results. When in vacuo charges are used DGhyd is,

as expected, systematically overestimated, in agreement with

previously reported work.[15] This shows that the polarizing

effect of the solvent is a feature that should be considered for

molecules with several polar functional groups. It is, however,

worth noting that all charge methods overestimate DGhyd to a

Table 1. Free energies of hydration with the four different charge models with effectively polarized charges (Pol.) and gas phase charges (Gas).

Compound

CHELP CHELPG MK RESP

Pol. Gas Pol. Gas Pol. Gas Pol. Gas Exp.

4-Nitroaniline �65.4 6 0.4 �27.1 6 0.3 �70.9 6 0.3 �34.2 6 0.5 �78.3 6 0.4 �37.3 6 0.5 �54.2 6 0.4 �32.7 6 0.4 �41.4 6 1.8 [77]

Aspirin �54.1 6 0.6 �29.2 6 0.5 �57.3 6 0.5 �48.6 6 0.4 �61.9 6 0.5 �36.3 6 0.4 �51.3 6 0.6 �29.6 6 0.5 �51.6 6 0.8 [77]

Caffeine �71.8 6 0.3 �40.8 6 0.4 �89.1 6 0.4 �67.9 6 0.4 �90.3 6 0.4 �73.7 6 0.5 �69.1 6 0.4 �49.7 6 0.6 �53.7 6 0.6 [77]

D-glucose �73.7 6 0.5 �68.7 6 0.7 �126.8 6 0.7 �73.2 6 0.6 �128.3 6 0.7 �89.0 6 0.5 �95.9 6 0.9 �81.1 6 0.8 �106.5 6 0.9 [77]

Diflunisal �31.4 6 0.5 �37.7 6 0.7 �33.6 6 0.4 �32.4 6 0.5 �37.5 6 0.6 �34.9 6 0.6 �39.1 6 0.7 �11.6 6 0.6 �31.0 6 1.2 [77]

Ethyl paraben �40.6 6 0.4 �19.3 6 0.4 �56.0 6 0.6 �28.0 6 0.5 �58.6 6 0.5 �29.1 6 0.4 �35.9 6 0.5 �21.2 6 0.4 �38.5 6 0.4 [77]

Glycerol �64.8 6 0.3 �40.1 6 0.3 �74.2 6 0.5 �46.0 6 0.4 �76.8 6 0.3 �48.3 6 0.4 �57.9 6 0.5 �44.0 6 0.4 �58.3 6 0.2 [77]

Uracil �116.7 6 0.4 �65.1 6 0.3 �112.0 6 0.3 �61.5 6 0.3 �110.4 6 0.3 �59.3 6 0.3 �80.7 6 0.4 �54.0 6 0.4 �67.2 6 1.2 [77]

Amrinone �95.6 6 0.4 �44.6 6 0.4 �119.0 6 0.4 �57.5 6 0.5 �126.0 6 0.3 �60.4 6 0.4 �91.9 6 0.4 �56.9 6 0.5 –

Benzyl benzoate �20.8 6 0.6 �6.9 6 0.6 �25.4 6 0.5 �7.1 6 0.5 �39.7 6 0.5 �16.8 6 0.3 �27.5 6 0.5 �16.5 6 0.6 –

Metformin �111.8 6 0.8 �73.1 6 0.7 �102.1 6 0.6 �61.9 6 0.7 �108.0 6 0.6 �85.7 6 0.6 �71.0 6 0.7 �66.3 6 0.5 –

Mesalazine �76.5 6 0.3 �41.5 6 0.4 �97.6 6 0.4 �83.3 6 0.6 �105.3 6 0.6 �90.4 6 0.5 �63.0 6 0.8 �45.6 6 0.5 –

Oxazole �27.9 6 0.3 �11.8 6 0.3 �34.0 6 0.4 �15.6 6 0.3 �37.0 6 0.4 �17.1 6 0.4 �26.4 6 0.2 �16.3 6 0.3 –

RMS error 23.7 19.4 25.4 14.4 27.3 12.3 9.73 17.0 –

All free energies are shown in the unit kJ mol�1.

Figure 2. Correlation between experimental and computed free energies of hydration with effectively polarized charges a) and the relative errors b) and

for in vacuo charges, d) and e), respectively. In c) the molecular structure of the compounds are given.




smaller amount when polarization is ignored than the meth-

ods underestimate the same property when charge polariza-

tion is taken into account (with the exception of RESP). There-

fore, it is evident that the polarization contribution is

important, but including it by merely placing the molecule in

polarizable continuum and using the CHELP, CHELPG, or MK

will not bring the simulated results closer to experimental find-

ings. The method that performs the best with the dataset pre-

sented in Figure 1 is RESP together with effectively polarized

charges. The root-mean-square error (RMSE) is around 3.8 kBT

which is relatively small. On the other end of the spectrum,

MK and CHELPG with effectively polarized charges are with a

RMSE of 11 kBT and 9.8 kBT, respectively. This is in agreement

with the findings of Shivakumar et al.[18] who concluded that

GAFF/RESP performs better than GAFF/CHELPG. As it is clear

that effectively polarized charges overestimate the molecule’s

hydrophilicity and the neglect of polarization overestimates

the molecule’s hydrophobicity, a middle way would be to pre-

fer. The reason for why the RESP methods work well could be

due to error cancellation. There is a nonuniqueness problem

whenever point charges are assigned to reproduce the quan-

tum mechanically determined ESP. The reason for the RESP

method to work so well here could be due the fact that the

ESP is well reproduced simultaneously as the charges are kept

as small as possible. The other methods lack this penalty func-

tion that tries to keep the magnitudes of the charges down

and therefore give too hydrophilic molecules although they

can still reproduce the ESP. One interesting observation is that

MK charges work relatively well if no polarization is taken into

account (a RMSE of 4.6 kBT).

Compounds that appear to be difficult contain functional

groups with nitrogen, for which the molecules’ hydrophilicity

is rather overestimated. It is also for these types of compounds

that the spread in free energy is the largest. In the SAMPL2

blind test, D-glucose, caffeine, and diflunisal were pointed out

as difficult compounds.[77] As can be seen in Table 1, RESP

with polarized charges performs quite well for these com-

pounds. The largest error is for caffeine and it is likely that

high density of electronegative species in these molecules

poses a problem for all charge determining methods.

The reason for why the applied charge computation meth-

ods give such a spread in free energies of hydration is difficult

to point out. A possible expla-

nation could be how the meth-

ods sample the ESP.[76] Most

methods only explore and try

to reproduce the QM ESP at

relative short distance from the

vdW surface of the molecule

despite the long-range nature

of Coulomb interactions. This

means that the point charges

are assured only to describe

the interactions between the

solute and the solvent at a

short distance. It is not certain

that the interactions at longer

distances are represented well by these partial atomic charges.

Another interesting point to make with charges is at which

QM level of theory the ESP was computed at. Often the Har-

tree-Fock method combined with the 6-31G(d) basis set is

used despite the fact that there are several available methods

for treating electron correlation that comes at a relatively low-

computational cost. It would be along one’s intuition that the

more accurate wave function is, the more accurate the ESP is

and hence the more accurate the partial atomic charge should

be. In a rather recent investigation, Mobley et al.[14] investigate

the impact of QM level of theory and draw the conclusions

that the dipole and multipole moments vary quite substan-

tially with the applied QM method. These effects together

with the LJ parameters were considered to be possible sources

of the discrepancy between simulations and experiments.

Extended simulations and molecular conformations

D-glucose and glycerol are difficult compounds due to their

flexibility and therefore one has to sample large parts of the

configurational space of these molecules to obtain a well-

defined free energy of hydration. To test the convergence of

the computed free energies, EEMD simulations were per-

formed with different lengths: 12, 14, 16, 18, 20, and 30 ns

where the first 10 ns were used to equilibrate the balancing

factors used in the EE scheme. Three molecules were consid-

ered, caffeine, D-glucose, and glycerol. The two latter were

chosen due to their flexibility and the former due to its rigid-

ity. This allows us to see if the simulation time is long enough

to sample a more complicated configurational space by compar-

ing the convergence of the free energy of solvation to that of a

molecule with less degrees of freedom. The results are pre-

sented in Table 2. As can be seen for DGhyd, the values do not

vary significantly which indicates that the free energies of hydra-

tion converge in simulations shorter than the 20 ns that were

first proposed here. The biggest impact is seen on the statistical

uncertainty as the free energy has converged. This is in agree-

ment with the findings of Paluch et al.[30] who used the EE

method to compute free energies of hydration for amino acid

analogs. This proves that the EE method is a robust method

that can provide accurate free energies within simulations of

shorter length than other previously mentioned methods.

Table 2. Convergence of computed free energies of solvation with increasing sampling time.

Caffeine D-glucose Glycerol

Sampling

time[a] DGhyd DGoct DGhyd DGoct DGhyd DGoct

12 �69.5 6 1.2 �66.7 6 4.9 �94.1 6 0.9 –[b] �58.7 6 0.7 �48.4 6 1.6

14 �69.4 6 1.4 �65.2 6 3.3 �93.7 6 1.5 –[b] �57.5 6 0.6 �47.2 6 1.0

16 �69.4 6 1.0 �63.2 6 2.0 �96.2 6 1.1 �58.6 6 3.0 �58.5 6 0.8 �47.0 6 1.0

18 �70.0 6 1.0 �68.2 6 3.0 �96.1 6 1.1 �58.6 6 3.0 �58.6 6 0.8 �47.8 6 0.9

20 �69.1 6 0.6 �68.7 6 2.7 �95.9 6 0.9 �73.4 6 1.4 �57.9 6 0.5 �49.1 6 1.0

30 �68.7 6 0.5 �69.0 6 1.0 �96.5 6 0.7 �80.1 6 1.2 �58.1 6 0.4 �50.6 6 0.8

Exp. �53.7 6 0.2[77] �53.3[c] �106.5 6 0.2[77] �88.0[c] �58.3 6 0.2[77] �43.7[c]

[a] Including a 10 ns equilibration of the EE balancing factors. [b] Insufficient sampling. [c] Calculated from

the experimental log P.

All energies are shown in kJ mol�1 and sampling time in ns.



Other functional groups such as carboxylic acids have been

proven to be difficult to obtain converged results for due the

tendency of the hydroxyl hydrogen to be kinetically trapped

in either a cis or trans conformation with respect to the car-

bonyl oxygen.[16,31] To make sure that sampling of all thermally

relevant points in phase space was sufficient, a number of sim-

ulations of aspirin in water were performed. By choosing dif-

ferent starting conformations (either cis or trans) for the EEMD

simulations, the convergence of this degree of freedom can be

checked although there exist more sophisticated methods.[31]

As can be seen in Figures 3a and 3b, there is a difference in

the free energy of hydration for these starting conformations,

but as the simulations are longer, this difference more or less

disappears. The torsion angle changes repeatedly between a

cis or trans conformation and as a result, the starting confor-

mation is of less importance. Therefore, it is safe to conclude

that the problem concerning ergodicity is not present in our

simulations if they are run for a sufficient amount of time. This

is somewhat different from earlier finding in the literature

where the free energy barrier to cross between these confor-

mations was too high for any simulation on a ns-timescale to

pass.[16] The reason for this is probably the difference in stud-

ied systems. Klimovich and Mobley looked an isolated carbox-

ylic acid where in our investigations all the carboxylic groups

are in the vicinity of another polar group, making intramolecu-

lar hydrogen bonds possible. As a consequence of this, direct

comparisons are somewhat difficult.

The potential presence of intermolecular hydrogen bonds

further complicates the charge calculations. While computing

charges from molecular structures that have been optimized

in gas phase, it is very likely that the charges are derived from

a molecular conformation that is not representative of the

structure in condensed phase. In the case of aspirin, there is a

possibility of an intramolecular hydrogen bond, see Figure 3d.

In an aqueous solution, this hydrogen bond is very likely to be

broken in order for aspirin to form more hydrogen bonds with

the surrounding water. This poses a problem as it is not

always easy to beforehand choose the correct molecular ge-

ometry to use for computing the charges with. Multiple con-

formations can be used, but it is possible that conformations

that are not relevant for the condensed phase are included

then. As can be seen in Figures 3c and 3d, the charges

between the two geometries do not deviate significantly from

each other, yet the difference in DGhyd is around 12 kJ mol�1.

Our simulations dismiss the intramolecular hydrogen bond

when aspirin is dissolved in water (data not shown) and

indeed the charges obtained from the geometry without this

interaction provide free energies of hydration in excellent

agreement with experimental findings. An important conclu-

sion from this is that great caution not only has to be applied

when choosing the method to obtain the partial atomic

charges but also when choosing from which molecular geom-

etry to compute them from.

Sampling issues are more evident for solvation in octanol.

For caffeine, DGoct converges to a value of roughly �69 kJ

mol�1 but for the other two compounds, especially D-glucose,

the sampling time has an impact on the free energy of solva-

tion. D-glucose has many internal degrees of freedom and as

the dynamics in the octanol system is slower compared to the

aqueous system, the sampling of phase space is not very effi-

cient. When the production of EEMD simulations for D-glucose

Figure 3. Free energy of hydration for aspirin as a function of simulation

time with different starting conformations and charges. In a) the charges

are taken from c) and in b) the charges are taken from d). cis and trans

correspond to different initial positions of the hydrogen of the hydroxyl

group relative the carbonyl oxygen. For all calculations, an initial 10 ns pe-

riod of equilibration of the balancing factors is included.




was prolonged even further than presented in Table 2, namely

to 40, 60, and 80 ns DGoct did not change, �79.2 6 1.2,

�79.17 6 1.0, and �79.8 6 0.9 kJ mol�1, respectively. Caf-

feine, on the other hand, is a rigid molecule with less internal

degrees of freedom and DGoct does not change drastically

between the different simulations. To ensure proper sampling

of the systems, dynamic properties were computed. The orien-

tational correlation time of octanol’s dipole was determined to

roughly 107 ps and the diffusion coefficient for the center of

mass of octanol in the octanol/water mixture was 0.081 �10�5cm2 s�1. From these results, we can conclude that sam-

pling in octanol is slow but not insufficient as the octanol mol-

ecules have time to decorrelate and diffuse. However, longer

simulations are to prefer as shown by the D-glucose simula-

tions for molecules with greater internal degrees of freedom.

Impact of solvent model

The impact of water model can affect the free energy of

hydration to large extents as noted by Shirts and Pande[78]

and Hess and van der Vegt.[11] To quantify this dependency in

the current manuscript, free energies of hydration were com-

puted for caffeine, glucose, glycerol, 4-nitroaniline, and ethyl

paraben using two popular water models, namely TIP3P and

SPC/E. For these simulations, all bonds were constrained and a

single time step of 2 fs was used. Other simulation parameters

were identical to those used for the fSPC calculations. The

results are presented in Table 3. As can be seen, the fSPC

water model results in a lower free energy of hydration in ev-

ery case except for ethyl paraben, which is the least hydro-

philic molecule of the this test. The possibility for the fPSC

water model to change its dipole moment is most likely the

reason for this. Due to fact that the fSPC water molecule can

alter its dipole moment, polarization effects are to a certain

extent taken into account.

In comparison with the values published by Klimovich and

Mobley[16] for caffeine, our values are consistently lower for the

polarized charge distributions and higher for the gas phase

charges. When comparing the values for glycerol in Table 3 to

the previously mentioned investigation, it is clear that the mole-

cule is more hydrophilic in the present investigation. The same

can be said for D-glucose. For the two latter compounds, the use

of effectively polarized charges brings the computed DGhyd val-

ues closer to the experiments and shows that inclusion of polar-

ization is important (as the charges used in ref. 16 were taken

from gas phase and the corresponding DGhyd were too high).

The differences in DGhyd are somewhat larger than observed

before by Shirts and Pande[78] and Hess and van der Vegt,[11]

but our drug molecules differ from the amino acid analogs

they studied. Furthermore, the strong dependency on the par-

tial atomic charges is shown by all water models which shows

that the conclusions previously drawn are valid, although the

trend is most evident with the fSPC model.

SAMPL2 blind test dataset

As the initial dataset was not of considerable size, we

extended our investigation by computing DGhyd for a larger

set of molecules, namely the one introduced in the SAMPL2

blind test.[77] It should be mentioned that one molecule,

5-iodouracil, was left out of the these simulations. Charges for

this set of molecules were computed with the methods

regarded to be the best from the previous section, that is, the

RESP method with effectively polarized charges. As the mole-

cules present in the SAMPL2 blind test are more heterogenous

and contain more functional groups this would provide more

insight to whether the conclusions drawn from the earlier,

Table 3. Impact of water model on the free energy of hydration.

Water model

Charges fSPC TIP3P SPC/E

Caffeine

CHELP �40.8 6 0.4 �41.1 6 0.5 �42.1 6 0.4

CHELPp �71.8 6 0.3 �65.3 6 0.4 �66.7 6 0.4

CHELPG �67.9 6 0.4 �67.7 6 0.5 �68.1 6 0.5

CHELPGp �89.1 6 0.4 �79.9 6 0.4 �81.9 6 0.5

MK �73.7 6 0.5 �66.1 6 0.4 �67.7 6 0.5

MKp �90.3 6 0.4 �81.5 6 0.5 �84.1 6 0.5

RESP �49.7 6 0.6 �47.6 6 0.5 �48.8 6 06

RESPp �69.1 6 0.4 �64.9 6 0.5 �65.6 6 0.3

Experiment �53.7 6 0.6[77]

D-glucose

CHELP �68.7 6 0.7 �64.2 6 0.6 �65.4 6 0.6

CHELPp �73.7 6 0.5 �69.7 6 0.6 �71.1 6 0.6

CHELPG �73.2 6 0.6 �69.0 6 0.6 �68.1 6 0.7

CHELPGp �126.8 6 0.7 �113.3 6 0.6 �119.4 6 0.8

MK �89.0 6 0.5 �82.4 6 0.7 �84.5 6 0.6

MKp �128.3 6 0.7 �115.8 6 0.8 �119.5 6 0.7

RESP �81.1 6 0.8 �76.7 6 0.6 �77.9 6 0.7

RESPp �95.9 6 0.9 �86.0 6 0.6 �88.1 6 0.7

Experiment �106.5 6 0.9[77]

Glycerol

CHELP �40.1 6 0.3 �39.1 6 0.4 �37.9 6 0.4

CHELPp �64.8 6 0.3 �58.8 6 0.3 �60.2 6 0.5

CHELPG �46.0 6 0.4 �44.1 6 0.5 �45.3 6 0.5

CHELPGp �74.2 6 0.5 �67.2 6 0.6 �68.4 6 0.4

MK �48.3 6 0.4 �45.0 6 0.3 �44.7 6 0.5

MKp �76.8 6 0.3 �58.8 6 0.5 �62.3 6 0.6

RESP �44.0 6 0.4 �42.3 6 0.6 �43.1 6 0.5

RESPp �57.9 6 0.5 �50.6 6 0.4 �52.2 6 0.5

Experiment �58.3 6 0.2[77]

4-nitroaniline

CHELP �27.1 6 0.3 �30.4 6 0.4 �28.1 6 0.3

CHELPp �65.4 6 0.4 �64.2 6 0.3 �62.1 6 0.5

CHELPG �34.2 6 0.5 �57.5 6 0.4 �54.8 6 0.3

CHELPGp �70.9 6 0.3 �72.6 6 0.4 �70.6 6 0.4

MK �37.3 6 0.5 �39.0 6 0.5 �36.4 6 0.4

MKp �78.3 6 0.4 �75.3 6 0.4 �73.0 6 0.5

RESP �32.7 6 0.4 �36.1 6 0.3 �33.0 6 0.5

RESPp �54.2 6 0.4 �57.5 6 0.5 �54.8 6 0.4

Experiment �41.4 6 1.8[77]

Ethyl paraben

CHELP �19.3 6 0.4 �21.8 6 0.5 �22.1 6 0.3

CHELPp �40.6 6 0.4 �41.0 6 0.4 �41.7 6 0.5

CHELPG �28.0 6 0.5 �29.4 6 0.4 �28.7 6 0.6

CHELPGp �56.0 6 0.6 �55.4 6 0.5 �57.0 6 0.4

MK �29.1 6 0.5 �32.1 6 0.7 �31.5 6 0.4

MKp �58.6 6 0.5 �61.1 6 0.4 �63.1 6 0.4

RESP �21.2 6 0.4 �24.2 6 0.5 �24.9 6 0.4

RESPp �35.9 6 0.5 �37.8 6 0.5 �36.8 6 0.6

Experiment �38.5 6 0.4[77]

All values are reported in kJ mol�1 and the p-superscript indicates that

the charges were effectively polarized as described in the Methods sec-

tion. Charges with no superscript are from gas phase.



smaller dataset were correct. We refer the reader to the work

of Geballe et al.[77] for an overview of the compounds in the

SAMPL2 blind test.

In Figure 4, the correlation between simulated and experi-

mental free energies is shown. The trend is clear: for the more

hydrophilic molecules, the DGhyd tends to be underestimated,

whereas for the more hydrophobic or less hydrophilic mole-

cules, DGhyd is overestimated (except for the most hydrophilic

molecule D-glucose). The reason for the underestimations is

likely due to the overpolarization as seen in the previous sec-

tion. The overestimation for the less hydrophilic molecules,

such as hexacholorobenzene (21.2 kJ mol�1) and hexachloro-

ethane (10.4 kJ mol�1), which lack dipole moments is most

probably attributed to the lack of explicit polarization and

more complicated multipole interactions, which are difficult to

treat with fixed-charged FFs. The disagreement for these less

hydrophilic molecules goes along with the findings of the

analysis of the SAMPL2 predictions.[77] The earlier observation

that nitrogen-containing compounds were difficult was con-

firmed by these calculations as well. Especially, the uracils

were too hydrophilic even with effectively polarized charges

determined by the RESP method, which is in agreement to

most submissions to the SAMPL2 blind test. Another molecule

for which the deviation was large was sulfolane, for which

DGhyd was underestimated by 24.0 kJ mol�1 This possibly

identifies the same FF deficiencies for sulfur as observed by

Mobley et al.[15] who studied a larger set of molecules. The

RMSE for this dataset consisting of 30 molecules is around 3.9

kBT which is to be compared to the best explicit solvent MD

simulation submission which had a RMSE of 4.0 kBT. It should

stressed that the simulations presented here were run at a

temperature of 310 K (to mimic a physiological temperature)

and the values reported by Geballe et al.[77] are for 298 K, so

the entropy contribution to our calculations could be slightly

overestimated. The results clearly show that the charge assign-

ing scheme proposed here, together with our simulation

setup, to be the best one which performs well on this heter-

ogenous dataset that contain a large variety of functional

groups.

Partition coefficients

To further test the impact of effectively polarized atomic

charges, free energies of solvation in octanol were computed.

This was done to investigate the impact of polarization in a

solvent with a lower dielectric constant. From experimental oc-

tanol/water partition coefficients, the free energy of solvation

in octanol (DGoct) can be determined.

log P ¼ 1

2:303

DDGRT

(4)

where DDG ¼ DGhyd � DGoct. log P values are also important

as they describe the partitioning of drug molecules between a

hydrophilic and a hydrophobic phase. In pharmacological stud-

ies, log P values are of the outermost importance as they are

used to model the partitioning between aqueous parts of

biological systems (blood, cytosol etc.) and the cell mem-

branes (modeled by octanol) of orally administrated drugs. In

Figure 5, computed and experimental log P values are com-

pared. DDG was calculated from simulations using either the

same charges in both water and octanol (gas phase charges)

or with different charges in each solvent (effectively polarized

charges), one set of charges for the aqueous phase and

another for the octanol phase. As DGhyd was systematically

underestimated when charges were implicitly polarized, the

corresponding log P values are underestimated which means

that the molecules prefer the aqueous solvent over octanol.

Also, in agreement with previous observations, the use of in

vacuo charges results in too hydrophobic molecules. The

charge method that has the best agreement with experiments

is RESP with polarized charges which gives a RMSE of 1.3 log

P units and the method that performs worst is MK with unpo-

larized charges with a RMSE of 2.9 log P units. Interestingly,

the RMSE for RESP charges without the polarization is 1.4

log P units which is a small difference when compared with

the effectively polarized charges. This leads us to the conclu-

sion that error cancellations occur for this unpolarized charge

set as the RMSE differs so little between these two methods.

For the other tested charge methods, there was no evident

trend of an error cancellation. This is in agreement with the

work of Jorgensen et al.[79] who concluded that the free

energy of hydration solely was responsible for the differences

in log P values. The inclusion of the limited polarization of the

solute that octanol induces on solutes is therefore not as im-

portant as the polarization effects of water. Further, the vdW

forces have been identified as playing a major part in the sol-

vation in octanol due to the limited polarity.[32,80]

Conclusions

Free energies of hydration have been computed for a number

of drug-like molecules with classical MD simulations. The main

focus was on the impact of the partial atomic charges on free

Figure 4. Correlation between experimental and computed free energies

of hydration for the molecule set used in the SAMPL2 blind test.[77]

Charges used in the simulations were computed with the RESP method

and were effectively polarized.




energy calculations. As it is well-known that solvent can have

a pronounced polarization effect on the electron distribution

of solutes, atomic charges were obtained by performing QM

calculations in polarizable continuum and then minimizing the

difference between the QM ESP and the one obtained from

point charges. These lead to effectively polarized charges that

performed better than in vacuo charges when the RESP

method was applied. To further test this conclusion, the free

energies of hydration for 30 molecules of the SAMPL2 dataset

were computed which showed in a small deviation when com-

pared with experimental data. The polarization effects of less

polar solvent like octanol were also tested by computing log P

values and again the RESP method with effectively polarized

charges performed the best.

Some important conclusions can be drawn based on the

data presented here. First, the results presented here suggest

that RESP charges at the B3LYP/6-311þG(d,p) level of theory

with polarization effects taken into account perform well for

computing free energies of solvation together with the simula-

tion setup used here and use of fSPC water model as a sol-

vent. It does not seem unlikely that this is due to the hyper-

bolic penalty function in RESP which assures that the charges

are kept as small as possible in magnitude while they simulta-

neously reproduce the ESP. Most importantly, the impact of

partial atomic charges on simulations based on classical point-

charge FFs has been verified. The enormous spread in DGhyd

illustrates that atomic charges are not a set of parameters to

take lightly. They can affect the results of molecular simula-

tions significantly as there is no ‘‘black-box’’ method available

to obtain reliable charges, great caution has to be applied.

Acknowledgments

The authors are grateful to PDC Center for High Performance Com-

puting, Stockholm and also High Performance Computing Center

North (HPC2N), Umea for kindly supplying allocated computer time.

A.L wants to thank the Sardinian Visiting Professors program at the

University of Cagliari, Italy. F.M. acknowledges the Wenner-Gren

Foundation for funding for Visiting Professorship. The authors

would also like to thank the referees for many helpful comments.

Keywords: molecular dynamics � free energy � computational

drug design � expanded ensemble � atomic charges

How to cite this article: J. P. M. J€ambeckmbeck, F. Mocci, A. P.

Lyubartsev, A. Laaksonen, J. Comput. Chem. 2013, 34, 187–197.

DOI: 10.1002/jcc.23117

Additional Supporting Information may be found in the

online version of this article

[1] J. D. Chodera, D. L. Mobley, M. R. Shirts, R. W. Dixon, K. Branson, V. S.

Pande, Curr. Opin. Struct. Biol. 2011, 21, 150.

[2] P. Kollman, Chem. Rev. 1993, 93, 2395.

[3] C. Chipot, D. A. Pearlman, Mol. Simul. 2002, 28, 1.

[4] M. R. Shirts, D. L. Mobley, J. D. Chodera, Annu. Rep. Comput. Chem.

2007, 3, 41.

[5] J. Westergren, L. Lindfors, T. H€oglund, K. Luder, S. Nordholm, R. Kjel-

lander, J. Phys. Chem. B 2007, 111, 1872.

[6] A. Leo, C. Hansch, D. Elkins, Chem. Rev. 1971, 71, 525.

[7] I. V. Tetko, V. Y. Tanchuk, A. E. Mark, J. Chem. Inform. Comput. Sci.

2001, 41, 1407.

[8] C. D. Christ, A. E. Mark, W. F. van Gunsteren, J. Comput. Chem. 2009,

31, 1569.

[9] J. G. Kirkwood, J. Chem. Phys. 1935, 3, 300.

[10] M. R. Shirts, J. W. Pitera, W. C. Swope, V. S. Pande, J. Chem. Phys. 2003,

119, 5740.

[11] B. Hess, N. F. A. van der Vegt, J. Phys. Chem. B 2006, 110, 17616.

[12] N. M. Garrido, A. J. Queimada, M. Jorge, E. A. Macedo, I. G. Economou,

J. Chem. Theory Comput. 2009, 5, 2346.

[13] C. H. Bennett, J. Comput. Phys. 1976, 22, 245.

[14] D. L. Mobley, E. Dumont, J. D. Chodera, K. A. Dill, J. Phys. Chem. B

2007, 111, 2242.

[15] D. L. Mobley, C. I. Bayly, M. D. Cooper, M. R. Shirts, K. A. Dill, J. Chem.

Theory Comput. 2009, 5, 350.

[16] P. V. Klimovich, D. L. Mobley, J. Comput. Aided Mol. Des. 2010, 24, 307.

[17] R. W. Zwanzig, J. Chem. Phys. 1954, 22, 1420.

[18] D. Shivakumar, Y. Deng, B. Roux, J. Chem. Theory Comput. 2009, 5, 919.

[19] D. Shivakumar, J. Williams, Y. Wu, W. Damm, J. Shelley, W. Sherman,

J. Chem. Theory Comput. 2010, 6, 1509.

[20] A. P. Lyubartsev, A. A. Martsinovski, S. Shekunov, P. N. Vorontsov-

Velyaimnov, J. Chem. Phys. 1992, 96, 1776.

[21] A. P. Lyubartsev, A. Laaksonen, P. N. Vorontsov-Velyaimnov, Mol. Phys.

1994, 82, 455.

Figure 5. Correlation between experimental and computed log p values.

Experimental log p values are taken from the PHYSPROP database.[81]



[22] A. P. Lyubartsev, A. Laaksonen, P. N. Vorontsov-Velyaimnov, Mol. Simul.

1996, 18, 43.

[23] A. P. Lyubartsev, S. P. Jacobsson, G. Sundholm, A. Laaksonen, J. Phys.

Chem. B 2001, 105, 7775.

[24] K. M. Aberg, A. P. Lyubartsev, S. P. Jacobsson, A. Laaksonen, J. Chem.

Phys. 2004, 120, 3770.

[25] E. C. Cichowski, T. R. Schmidt, J. R. Errington, Fluid Phase Equilib. 2005,

236, 58.

[26] J. K. Shah, E. J. Maginn, J. Phys. Chem. B 2005, 109, 10395.

[27] F. J. Martinez-Veracoechea, F. A. Escobedo, J. Phys. Chem. B 2008, 112,

8120.

[28] J. Chang, J. Chem. Phys. 2009, 131, 074103.

[29] A. S. Paluch, S. Jayaraman, J. K. Shah, E. J. Maginn, J. Chem. Phys.

2010, 133, 124504.

[30] A. S. Paluch, J. K. Shah, E. J. Maginn, J. Chem. Theory Comput. 2011, 7,

1394.

[31] A. S. Paluch, D. L. Mobley, E. J. Maginn, J. Chem. Theory Comput. 2011,

7, 2910.

[32] E. M. Duffy, W. L. Jorgensen, J. Am. Chem. Soc. 2000, 122, 2878.

[33] Y. Deng, B. Roux, J. Phys. Chem. B 2004, 108, 16567.

[34] U. C. Singh, P. A. Kollman, J. Comput. Chem. 1984, 5, 129.

[35] L. E. Chirlian, M. M. Francl, J. Comput. Chem. 1987, 8, 894.

[36] C. M. Breneman, K. B. Wiberg, J. Comput. Chem. 1990, 11, 361.

[37] B. H. Besler, K. M. Merz, P. A. Kollman, J. Comput. Chem. 1990, 11, 431.

[38] M. M. Francl, C. Carey, L. E. Chirlian, D. M. Gange, J. Comput. Chem.

1996, 17, 367.

[39] M. M. Francl, L. E. Chirlian, Rev. Comput. Chem. 2000, 14, 1.

[40] C. A. Reynolds, J. W. Essex, W. G. Richards, J. Am. Chem. Soc. 1992,

114, 9075.

[41] W. D. Cornell, P. Cieplak, C. I. Bayly, P. A. Kollman, J. Am. Chem. Soc.

1993, 115, 9620.

[42] M. Basma, S. Sundara, D. Calgan, T. Vernalli, R. J. Woods, J. Comput.

Chem. 2001, 22, 1125.

[43] J. W. Essex, C. A. Reynolds, W. G. Richards, J. Am. Chem. Soc. 1992,

114, 3634.

[44] C. A. Reynolds, J. W. Essex, W. G. Richards, Chem. Phys. Lett. 1992, 199,

257.

[45] S. G. Lister, C. A. Reynolds, W. G. Richards, Int. J. Quantum Chem. 1992,

41, 293.

[46] C. I. Bayly, P. Cieplak, W. D. Cornell, P. A. Kollman, J. Phys. Chem. 1993,

97, 10269.

[47] W. C. Swope, H. W. Horn, J. E. Rice, J. Phys. Chem. B 2010, 114, 8621.

[48] W. C. Swope, H. W. Horn, J. E. Rice, J. Phys. Chem. B 2010, 114, 8631.

[49] C. Chipot, J. Comput. Chem. 2002, 24, 409.

[50] D. L. Mobley, E. Dumont, J. D. Chodera, K. A. Dill, J. Phys. Chem. B

2011, 115, 1329.

[51] D. L. Mobley, S. Liu, D. S. Cerutti, W. C. Swope, J. E. Rice, J. Comput.

Aided Mol. Des. 2012, 26, 551.

[52] J. Wang, R. M. Wolf, J. W. Caldwell, P. A. Kollman, D. A. Case, J. Comput.

Chem. 2004, 25, 1157.

[53] S. H. Vosko, R. G. Wilk, M. Nusair, Can. J. Phys. 1980, 58, 1200.

[54] C. Lee, W. Yang, R. G. Parr, Phys. Rev. B 1988, 37, 785.

[55] A. D. Becke, J. Chem. Phys. 1993, 98, 5648.

[56] P. J. Stephens, F. J. Devlin, C. F. Chabalowski, M. J. Frisch, J. Chem.

Phys. 1995, 98, 11623.

[57] V. Barone, M. Cossi, J. Tomasi, J. Comput. Chem. 1998, 19, 404.

[58] M. Cossi, N. Rega, G. Scalmani, V. Barone, J. Comput. Chem. 2003, 24,

669.

[59] M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J.

R. Cheeseman, G. Scalmani, V. Barone, B. Mennuci, G. A. Peterson, H.

Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmayov, J. Bloino, G.

Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J.

Hasegawa, M. Ishilda, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T.

Montgomery Vreven, J. A. Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J.

Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Nor-

mand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi,

M. Cossi, N. Rega, J. M. Milliam, M. Klene, J. E. Knox, J. B. Cross, V.

Bakken, C. Adamo, J. Jaramillo, R. gomperts, R. E. Stratmann, O. Yazyev,

A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Moro-

kuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S.

Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslow-

ski, D. J. Fox, Gaussian09, Revision A.02, Gaussian Inc., Wallingford CT,

2009.

[60] F. Y. Dupradeau, A. Pigache, T. Zaffran, C. Savineau, R. Lelong, N. Grivel,

D. Lelong, W. Rosanski, P. Cieplak, Phys. Chem. Chem. Phys. 2010, 12,

7821.

[61] G. S. Maciel, E. Garcia, Chem. Phys. Lett. 2005, 409, 29.

[62] F. De Proft, J. M. L. Martin, P. Geerlings, Chem. Phys. Lett. 1996, 250,

393.

[63] S. Tsuzuki, T. Uchimaru, K. Tanabe, A. Yliniemela, J. Mol. Struct. (Theo-

chem) 1996, 365, 81.

[64] K. Toukan, A. Rahman, Phys. Rev. B 1985, 31, 2643.

[65] A. M. Nikitin, A. P. Lyubartsev, J. Comput. Chem. 2007, 28, 2020.

[66] H. J. C. Berendsen, J. R. Grigera, T. P. Straatsma, J. Chem. Phys. 1987,

91, 6269.

[67] W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R. W. Impey, M. L.

Klein, J. Chem. Phys. 1983, 79, 926.

[68] A. P. Lyubartsev, O. K. Forrisdahl, A. Laaksonen, J. Chem. Phys. 1998,

108, 227.

[69] F. Wang, D. P. Landau, Phys. Rev. Lett. 2001, 86, 2050.

[70] B. A. Berg, T. Neuhaus, Phys. Rev. Lett. 1992, 68, 9.

[71] J. Lee, Phys. Rev. Lett. 1993, 71, 211.

[72] S. Nos�e, Mol. Phys. 1984, 52, 255.

[73] W. G. Hoover, Phys. Rev. A 1985, 31, 1695.

[74] M. E. Tuckerman, B. J. Berne, G. J. Martyna, J. Chem. Phys. 1992, 97,

1990.

[75] A. P. Lyubartsev, A. Laaksonen, Comput. Phys. Commun. 2000, 128, 565.

[76] E. Sigfridsson, U. Ryde, J. Comput. Chem. 1998, 19, 377.

[77] M. T. Geballe, A. G. Skillman, A. Nicholls, J. P. Guthrie, P. J. Taylor,

J. Comput. Aided Mol. Des. 2010, 24, 259.

[78] M. R. Shirts, V. S. Pande, J. Chem. Phys. 2005, 122, 134508.

[79] W. L. Jorgensen, J. M. Briggs, M. L. Contreras, J. Phys. Chem. 1990, 94,

1683.

[80] P. Cieplak, J. Caldwell, P. Kollman, J. Comput. Chem. 2001, 22, 1048.

[81] PHYSPROP, Physical/Chemical Property Database; Syracuse Research

Corporation, SRC Environmental Research Centre: New York, 1994.

Received: 12 March 2012Revised: 23 August 2012Accepted: 24 August 2012Published online on 20 September 2012




Partial atomic charges and their impact on the free energy of solvation

Documents