partial atomic charges 
 are an integral part of today s molecular 
 mechanic force fields .
although force 
 fields that involve more rigorous potential energy functions , such 
 as those including polarizability or multipole electrostatics , are 
 growing in popularity and availability , fixed - charge 
 force fields continue to receive extensive use for modeling condensed - phase 
 systems .
the increasing role of computational chemistry in 
 drug discovery and biological modeling often requires the ability 
 to model an arbitrary molecule which has not been explicitly parametrized . 

while intramolecular and lennard - jones parameters are often easily 
 estimated or transferable for new organic functional groups or heterocycles , 
 the assignment of partial atomic charges is not obvious .
if experimental data are available , force fields 
 can be parametrized specifically for these molecules , to reproduce 
 liquid - state properties , but this situation is generally rare for 
 many components of drugs such as heterocycles . alternatively
, quantum 
 mechanical ( qm ) calculations can be performed , whereby atomic charges 
 are derived from the wave functions to reproduce gas - phase dipole 
 moments or electrostatic potentials . for use with fixed - charge models in condensed - phase 
 simulations , it is then necessary to scale the gas - phase charges to 
 take into account polarization effects in an average sense .
optimization of the scaling factors often focuses on minimizing 
 errors in computed free energies of hydration . in 2004 ,
charge 
 models 1 and 3 ( cm1 & cm3 ) were tested for their 
 utility in condensed - phase simulations .
charges were computed in conjunction with am1 and pm3 semiempirical 
 quantum methods ( creating the cmxa and cmxp models ) and tested for their accuracy to reproduce experimental 
 free energies of hydration for 25 neutral organic molecules .
optimal scaling 
 factors of 1.14 and 1.15 were shown to give the lowest mean unsigned 
 errors ( mues ) of 1.03 and 1.13 kcal / mol for cm1a and cm3a , respectively . 
 due to the better performance of the 1.14*cm1a charges in reproducing 
 free energies of hydration for amides ,
this method was taken to be 
 preferred for simulations of biomolecular systems in explicit water . since the introduction of the cm1a and 
 cm1p charge models in 1995
, 
 successive refinements have been made to produce charge models ( cmx ) 2 , 3 , 4 , and 4 m .
these charge models transform mulliken , lwdin , or redistributed 
 lwdin population analyses to 
 derive atomic charges capable of accurately reproducing experimental 
 gas - phase dipole moments .
most recently , charge model 5 ( cm5 ) was published , which utilizes gas - phase atomic 
 charges from a hirshfeld population analyses . in that report
, hirshfeld charges were shown to be less sensitive 
 to basis set size than lwdin or mulliken charges and more 
 consistent across a wide range of electronic structure methods .
these 
 characteristics are maintained in cm5 , allowing the model to consist 
 of only a single set of parameters for various combinations of electronic 
 structure methods and basis sets .
cm5 parameters were fit using a 
 test set of 614 neutral molecules containing 26 different elements 
 ( h  ca , zn , ge  br , and i ) and were extended to every 
 element in the periodic table via recursive fitting ; the mean unsigned 
 error is only 0.26 d. thus , a new charge model has been created for 
 potential use for an enormous range of molecules and applications . with the noted success of cm5 for reproducing gas - phase electrostatic 
 properties ,
the present investigation was initiated to determine its 
 utility in the condensed phase , explicit solvent simulations .
free 
 energies of hydration provide an important measure for testing force 
 field parameters , especially atomic charges , as witnessed by the large 
 number of publications computing this property within the past few 
 years .
experimental data are available , and applications to larger systems 
 in chemistry , biology , and medicine are clear . in this report , free energies of hydration are computed initially 
 for an expanded set of 42 neutral , organic molecules to determine 
 an optimal scaling factor for cm5 charges .
free 
 energies of hydration obtained using the scaled cm5 charges are compared 
 with those derived from other charge methods including 1.14*cm1a and 
 opls - aa .
cm1a and 
 cm5 partial atomic charges were computed 
 via single point ( sp ) calculations on geometries optimized using the 
 boss program with the opls - aa force field .
this included the use of the nonbonded parameters for thiols and 
 sulfides , which were updated in 2001 .
hirshfeld atomic charges were obtained 
 from a m06 - 2x density function theory 
 ( dft ) single - point calculation using the 6 - 311+g(2df,2p ) basis set in conjunction with a hirshfeld population analysis 
 in gaussian 09 , revision a.02 .
cm5 charges 
 were then calculated with the cm5pac software , which uses the hirshfeld 
 charges from the gaussian output file .
it should be noted that in the course of completing this study , 
 gaussian 09 revision d.01 was released , which automatically incorporates a cm5 charge calculation with every 
 hirshfeld population analysis .
the cm1a and cm5 charges were averaged 
 as usual for equivalent atoms , e.g. , hydrogen atoms in a methyl group . 

this is necessary for force fields to avoid nonphysical asymmetries , 
 such as different energies for identical rotamers .
scaled cm1a and cm5 atomic charges for the molecules considered 
 here are recorded in table s1 of the supporting 
 information .
metropolis monte 
 carlo statistical mechanics in conjunction 
 with free energy perturbation ( mc / fep ) 
 calculations were carried out using boss to compute relative and absolute 
 free energies of hydration for the 42 molecules .
the fep calculations 
 were based upon the zwanzig equation ( eq 1 ) . the free energy difference between an initial 
 ( a ) and final state ( b ) of a system is calculated as an ensemble average 
 of the potential energy difference between states , sampled at the 
 initial state . to apply fep theory to chemical 
 equilibria ,
a thermodynamic cycle is employed ( scheme 1 ) in which the initial and final states could be different 
 molecules , conformers , or different force field parameters for the 
 same molecule .
conversion of a to b in two media , g1 and g2 , provides 
 the difference in free energy of transfer , gb  ga ( scheme 1 ) .
a difference in free energies of hydration can 
 be obtained by taking medium 1 as the gas phase and medium 2 as water . 
 to achieve good convergence ,
windows ,  categorized by 
 a coupling parameter , i ( eq 2 ) , which scales all geometrical and force field parameters , 
 i , as a transforms to b. such calculations 
 were first performed in 1985.12 in boss , two sampling schemes are implemented for computing 
 free - energy 
 differences , double - wide sampling ( dws ) and simple 
 overlap sampling ( sos ) .
both methods deliver 
 accurate results when more than 10 windows are used for molecular 
 transformations involving a single non - hydrogen atom , e.g. , ch3  h. in this work , both 
 sos and dws have been employed , as discussed below .
absolute free energies of hydration 
 can be computed in two ways . historically , relative molecular perturbations 
 between two molecules ( a and b in scheme 1 ) 
 have been favored due to their precision and viable computational 
 expense .
if changes between a and b are 
 small , then sufficient convergence is achieved using ca .
relative free energy values can then be added to a reference 
 absolute free energy to derive new absolute free energies .
this works 
 well when only a few transformations are needed to connect to the 
 reference molecule , often methane or benzene ; however , errors accumulate 
 for longer sequences of transformations . the alternative approach 
 is to perform complete molecular annihilations ,
these calculations make the entire molecule  disappear  
 from a medium by scaling all nonbonded force - field parameters to zero . 
 while demanding long molecular dynamics or monte carlo runs and small 
 fep steps , these calculations provide a means to calculate an absolute 
 free energy of solvation for any molecule , independent of previous 
 calculations .
the statistical uncertainties in the results can also 
 be systematically reduced by increasing the averaging periods .
all mc / fep 
 calculations were carried out with boss and closely followed previously 
 reported procedures .
a single 
 solute was placed in a cubic box with 500 water molecules , and simulations 
 were conducted at 25 c and 1 atm in the isothermal  isobaric 
 ensemble .
solvent  solvent and solute  solvent cutoff 
 distances , rc , for calculating nonbonded 
 interactions were set at 10  based on all non - hydrogen atom 
 pairs ; i.e. , if any heavy atom  heavy atom distance is below rc , the entire intermolecular interaction is 
 evaluated .
as before , the intermolecular 
 interactions are quadratically feathered to zero over the last 0.5 
  based on the shortest heavy atom  heavy atom distance , rm ; the scaling factor is ( rc  rm)/(rc  rl ) where rl = rc  0.5 .
all internal 
 degrees of freedom were sampled for the solute , while tip4p water 
 molecules underwent rigid - body translations and rotations .
solute 
 and volume moves were attempted every 100 and 3125 configurations , 
 respectively .
ranges for translations and rotations of 0.06 
  and 6.0 for solutes and 0.15  and 15.0 
 for the water molecules were chosen to produce mc acceptance rates 
 of ca .
dummy atoms were used when 
 perturbations were performed between molecules with different numbers 
 of atoms .
dummy atoms have zero valued 
 nonbonded parameters , equilibrium bond lengths of 0.30  , and 
 force constants for bond stretching and angle bending as in their 
 real counterparts .
statistical uncertainties ( 1 ) were 
 calculated from the batch means procedure using batch sizes of 1 m 
 configurations ; additional tests of precision 
 are described below . for all ghyd calculations ,
final uncertainties are below 0.25 kcal / mol , which 
 is comparable to typical experimental uncertainties of 0.3 kcal / mol .
this work began by computing ghyd for the 42 molecules using 1.14*cm1a and opls - aa charges 
 in the 
 a  b manner .
twenty - one windows of simple overlap sampling 
 ( 21-sos ) with 5 million configurations of equilibration and averaging 
 ( 5m/5 m ) in the gas phase and 15m/30 m configurations in water were 
 used .
previously , 10 windows of dws ( 10-dws ) were carried out with 
 10m/2040 m configurations in water to compute ghyd for 25 molecules . in view of the success with sos procedures
, it was decided to recalculate all 1.14*cm1a and opls - aa results 
 with this sampling method to further assess precision . in this
regard , 
 it is informative to analyze results for closed fep cycles ; the sum 
 of the individual free energy changes for each cycle should be zero . 

as shown in table 1 , the mean signed errors 
 for the cycles using sos with both charge options are near zero ; the 
 mean unsigned errors ( mue ) are less than 0.15 kcal / mol , and the maximum 
 individual errors are no more than 0.24 kcal / mol .
absolute free energies 
 of hydration for all 42 molecules were computed in a series of perturbations 
 to methane .
methanol and acetone were used as intermediates for many 
 sequences , and aromatic compounds were perturbed to benzene , which 
 was converted to methane .
in addition to the relative free energy calculations , 
 full molecular 
 annihilations were performed for all molecules using the 1.14*cm1a 
 charges .
annihilations were accomplished by first neutralizing the 
 atomic charges and , in a separate calculation , diminishing the lennard - jones 
 parameters to zero .
for all annihilations , 21-sos windows with 8m/8 m 
 configurations in the gas phase and 35m/70 m configurations in water 
 were used .
as i progressed from 
 0  1 , each atom was transformed into a corresponding idealized 
 sp or sp dummy atom , and equilibrium bond 
 lengths were perturbed to 0.30  .
unique to the annihilations , 
 the sos sampling led to end - point problems when sampling occurred 
 at i = 1 , reminiscent of earlier 
 findings . in this case
, solute and solvent 
 molecules can occupy the same space , which introduces infinite nonbonded 
 energies into the energy difference e in eq 1 . to correct for this
, sos sampling was performed 
 up to i = 0.99 , at which point , 
 dws sampling was used to obtain the free - energy result for i = 0.99  1 by running from i = 0.995 to 0.99 and 1.0 .
computer time for 
 a single fep window averaged 30 min for the relative perturbations 
 and 70 min for the annihilations in water on an intel core2 quad 3.3 
 ghz processor .
charge perturbations 
 were then 
 executed to determine the ghyd results 
 using the cm5 charges .
1.14*cm1a charges were first perturbed to unscaled 
 cm5 charges ( 1.00*cm5 ) while keeping other force - field parameters 
 constant .
thus , 10 windows of double - wide sampling were 
 used featuring 5 million configurations for equilibration and averaging 
 for each window in the gas phase and 10m/15 m configurations in water . 

the cm5 charges were subsequently scaled in separate fep calculations 
 from 1.00*qcm5 to 1.50*qcm5 in steps of 0.01 , where qcm5 represents an atomic charge .
absolute free energies of hydration 
 were computed for each scaling , and the optimal scaling factor was 
 chosen to minimize the mean unsigned error for all 42 molecules .
absolute free energies of hydration were computed 
 using two cmx charge models and the opls - aa force 
 field for the initial 
 set of 42 molecules .
the absolute free energy of hydration of methane 
 was computed to be 2.51  0.07 kcal / mol via annihilation with 
 the 1.14*cm1a charges .
this value is in good agreement with previous 
 results of 2.32.6 kcal / mol for opls - based models and experiment ( 2.01 kcal / mol ) .
all other absolute free energies of hydration were anchored by this 
 value via relative fep transformations . in summary ,
a mean unsigned 
 error of 1.17 kcal / mol is obtained for the 42 absolute free energies 
 of hydration with the 1.14*cm1a charges . an optimal scaling factor 
 of 1.27
was determined for the cm5 charges , which yields a mue of 
 1.10 kcal / mol for ghyd .
table 2 compares the previous and recomputed 1.14*cm1a results ; table 3 records the full results for the 1.14*cm1a and 1.27*cm5 free energies 
 of hydration .
a more 
 thorough analysis is made in the discussion section and focuses on comparing the 1.14*cm1a and 1.27*cm5 results . 

in addition , results for 44 relative free - energy calculations , ghyd , which yielded mues of 1.08 and 0.66 kcal / mol 
 using the 1.14*cm1a and opls - aa charges , are listed in table s2 . from ref ( 13 ) : 8m/8 m gas - phase and 10m/2040 m aqueous - phase 
 configurations .
this work : 
 5m/5 m gas - phase and 15m/30 m 
 aqueous - phase configurations .
results obtained from a series of 
 fep / sos calculations ; computed uncertainties are less than 0.25 kcal / mol . in 2004 , the optimal 
 scaling factor of 1.14 for cm1a charges was determined from fitting 
 to free energies of hydration for 25 molecules using series of fep 
 calculations with 10 windows of dws .
the 
 cm1a results for these molecules were recalculated in this work with 
 21 windows of sos , and then the coverage was expanded to 42 molecules . 

overall , the dws and sos results are mostly the same 
 within the statistical limits of about 0.3 kcal / mol
. improvements 
 of around 0.50 kcal / mol or greater , nearer experimental values , are 
 noted for methanethiol and methyl acetate , while reductions in accuracy 
 of 0.50 kcal / mol or greater are found for acetonitrile , acetone , and 
 ( e)-n - methylacetamide .
the variations 
 in the results are in - line with previous findings ; they are attributed to the differences in numbers of windows 
 and run lengths , which favor the 21-sos procedure .
the net result 
 is an insignificant change in the overall mue from 1.03 to 1.06 kcal / mol . 

additional problem cases 
 are methanethiol , aniline , and pyridine with errors around 2 kcal / mol .
expanding the calculations from 25 to 42 molecules increases the 
 mue from 1.06 to 1.17 kcal / mol using the 1.14*cm1a charges ( table 3 ) .
the mue was not helped by the addition of nitrobenzene 
 and the methylanilines , which continue the pattern of being computed 
 to be too well hydrated with an error now of nearly 4 kcal / mol for 
 nitrobenzene .
for the added sulfur - containing molecules , the ghyd for dimethyl sulfide is too positive by 
 2.79 kcal / mol ; however , the errors for thiophenol and thioanisole 
 are less than 0.6 kcal / mol . the errors for most of the other new additions 
 are under 1.5 kcal / mol ( propene , methyl formate , fluorobenzene , bromobenzene , 
 benzonitrile , acetophenone , -methylstyrene , and methyl benzoate ) . 

the error for acetaldehyde is 1.57 kcal / mol , and it is 2.77 kcal / mol 
 for dimethyl sulfoxide . though the error for acetamide is only 0.43 
 kcal / mol , the newly added benzamide is computed to be too well hydrated 
 by 2.25 kcal / mol .
the results are plotted in figure 1 ; a linear fit gives an r of 
 0.87 for the correlation of the computed and experimental data .
correlation 
 between experimental and computed free energies of 
 hydration ( kcal / mol ) : 1.14*cm1a results ( top ) , 1.27*cm5 results ( bottom ) . 

the solid line shows the ideal y = x line ; the dashed line represents the best fit line for the computed 
 data . the optimal scaling 
 factor for the cm5 charges turned out to be 1.27 to minimize the mue 
 for the computed free energies of hydration .
the 1.27*cm5 results 
 in table 3 lead to mean signed and unsigned 
 errors of 0.49 and 1.10 kcal / mol , respectively .
the mue is a little 
 lower than for the 1.14*cm1a results ; however , the r for the linear fit to the experimental data in figure 1 improves to 0.95 from 0.87 .
it may be noted 
 that the choice of the cm5 scaling factor benefited from use of the 
 results for the full set of 42 molecules , while the cm1a scaling factor 
 was derived from the results for the original 25 molecules . for the 
 25 molecules , the mue is 0.96 kcal / mol using the 1.27*cm5 charges , 
 which is again a little lower than the mue of 1.06 kcal / mol with the 
 1.14*cm1a charges . in comparing several electrostatic - potential and 
 am1-based charge models , mobley and
co - workers suggested that a root - mean - square 
 error of ca .
1.0 kcal / mol may be the current limit 
 for fixed charge models in predicting free energies of hydration .
it 
 is apparent that some functionality is not well represented by the 
 single charged site per atom model .
as discussed more below , the principal 
 problems with the 1.27*cm5 charges occur for sulfur and halogen containing 
 molecules .
the cmx results are also compared 
 with published data from molecular dynamics calculations using am1-bcc / gaff 
 charges in tip3p water and opls_2005 charges in spc water in table 3 .
although results from other 
 methods exist for comparison , the chosen ones are viewed as relatively accurate .
the mean unsigned errors for the cmx models fall 
 between those for the opls_2005 and am1-bcc / gaff methods .
both cmx methods have signed errors less positive 
 than the opls_2005 and gaff results .
furthermore , the r values for the opls_2005 and gaff results are 0.96 and 
 0.92 versus the 0.87 and 0.95 for 1.14*cm1a and 1.27*cm5 . the results 
 can be easily biased by selective addition and removal of compounds , 
 e.g. , removal of nitro compounds for 1.14*cm1a and dmso for 1.27*cm5 . 

completion of the missing numbers in table 3 , e.g. , for dmso , the methyanilines , and thiophenol with opls_2005 , 
 can also be expected to affect the results , adversely in this case . 

overall , the results in table 3 for the different 
 methods can be viewed as similar and reflecting the 1 kcal / mol limit 
 for general charge methods .
dipole moments 
 were calculated for all molecules with the 1.14*cm1a , 1.27*cm5 , and 
 1.00*cm5 charges ( table 4 ) .
the charge scaling 
 for neutral molecules is needed to incorporate solute polarization 
 in an average sense for condensed phase modeling with fixed - charge 
 force fields .
as shown in table 4 , the unscaled cm5 charges yield excellent values for gas - phase 
 dipole moments with a mue of only 0.16 d. it is noted that some differences 
 occur between 1.00*cm5 dipole moments computed here and those in the 
 original cm5 report .
the differences 
 of 0.30 d or more for dmso , nitroethane , nitrobenzene , and n , n - dimethylacetamide 
 can be attributed to the variations in optimized geometries and electronic 
 structure methods used for the cm5 charge computations ( see tables s4 and s5 ) .
it is also apparent that in 
 comparing the 1.14*cm1a and 1.27*cm5 dipole moments , the larger scaling 
 factor for the cm5 charges does not always lead to higher dipole moments . 

the most striking exceptions are for amines and nitro compounds . the 
 lower dipole moments for methylamine and dimethylamine with the 1.27*cm5 
 charges do correlate with the overly positive computed free energies 
 of hydration ( table 3 ) , while the dipole moments 
 for the nitro compounds are clearly too large with the cm1a charges 
 and contribute to the far too favorable computed ghyd values .
the 1.14*cm1a 
 charges for nitrogen and oxygen are 0.68 and 0.46 , while they 
 are 0.54 and 0.37 with opls - aa and 0.11 and 0.23 with 
 1.27*cm5 . however
o bonds in dimethyl sulfoxide , too large dipole moments , 
 and too negative free energies of hydration .
mean unsigned 
 errors in ghyd for compound classes 
 are listed in table 5 to help identify systematic 
 strengths and weaknesses for the charge models .
the 1.27*cm5 model yields lower average errors than 
 the 1.14*cm1a 
 alternative for most classes except hydrocarbons and halogen and sulfur 
 containing molecules .
ghyd for 
 less polar benzene derivatives is uniformly too positive by 12 
 kcal / mol with 1.27*cm5 ( table 3 ) , which contributes 
 significantly to the errors for hydrocarbons and halides .
the clear 
 failing of the 1.14*cm1a charges is nitro compounds , while both cmx approaches show significant deviations for sulfur - containing 
 molecules .
dimethyl sulfoxide ( dmso ) is particularly problematic with 
 errors of 2.8 and 3.6 kcal / mol .
unfortunately , additional sulfoxides 
 and sulfones could not be tested due to a lack of experimental data . 

the 1.27*cm5 method shows higher unsigned errors for the sulfur - containing 
 molecules due to its larger deviations for thiophenol and thioanisole . 

there is no problem with the computed dipole moments ( table 4 ) , so it is in the details of the charge distributions . 
 for thiophenol ,
the thiol sulfur and hydrogen have charges of 0.14 
 and 0.16 with 1.14*cm1a and 0.21 and 0.17 with 1.27*cm5 .
these 
 differences are not striking , though the larger charge on sulfur would 
 diminish the hydrogen - bond donating ability of the thiol group .
however , 
 there is a general pattern that the charges on the carbons and hydrogens 
 in phenyl rings are smaller in magnitude with 1.27*cm5 than with 1.14*cm1a 
 by ca .
remarkably , this 
 translates to less favorable free energies of hydration for benzene , 
 toluene , and -methylstyrene by 1.21.5 kcal / mol with 
 1.27*cm5 ( table 3 ) and presumably a similar 
 offset for the other substituted benzenes .
additional insights 
 can be obtained by considering computed interaction 
 energies for some hydrogen - bonded complexes in the gas phase .
results 
 are reported in table 6 for nine representative 
 complexes using opls - aa and the opls / cmx models .
opls - aa interaction 
 energies correlate well with high - end ab initio results and are given for comparison .
the variation 
 of the results for each of the nine complexes is notably small , within 
 1 kcal / mol for most cases . for both methanol and methanethiol , water 

is preferred as the hydrogen - bond donor by about 1 kcal / mol , and the 
 interactions are more favorable with the 1.27*cm5 charges than 1.14*cm1a 
 by a few tenths of a kilocalorie per mole . however , in both cases , 
 the free energies of hydration are too positive , though the results 
 are improved with 1.27*cm5 ( table 3 ) .
cbs - q 
 results for the four complexes of methanol and methanethiol in order 
 are 5.69 , 5.27 , 3.90 , and 2.50 kcal / mol , 
 and mp2/6 - 31++g(2d(x+),p ) gives very similar values .
thus , the raw interaction energies are not overly weak , 
 and the conclusion is that the effects of polarization in water are 
 not sufficiently compensated for by the charge scaling in these cases . 
 for dimethyl ether and dimethyl sulfide , the best ab initio and dft 
 results indicate interaction energies with water of about 5 
 and 4 kcal / mol , while the scaled 
 cmx results in table 6 are stronger and weaker , 
 respectively .
the consequences are reasonably computed ghyd values for dimethyl ether , but overly positive 
 results for dimethyl sulfide by about 2.7 kcal / mol . for dimethyl sulfide , 

the sulfur atom is not a sufficiently good hydrogen - bond acceptor 
 with the cmx charge models .
the larger size and increased polarizability 
 of sulfur relative to oxygen likely make its condensed phase electrostatics 
 more difficult to model with fixed charge approximations .
the free energies of hydration of aliphatic amides , a functional 
 group particularly important for biologically related studies , are 
 well reproduced by the 1.14*cm1a model ( table 3 ) . with the 1.27*cm5 charges , the ghyd values for acetamide and z - nma are too favorable 
 by 2.4 and 1.1 kcal / mol .
for the water  acetamide complexes 
 in table 6 , the hydrogen bonds to the carbonyl 
 oxygen are significantly stronger with 1.27*cm5 than with opls - aa 
 or 1.14*cm1a .
if the scaling factor for the cm5 charges were reduced 
 to 1.20 , the ghyd errors would 
 decrease to 0.58 kcal / mol for both acetamide and z - nma .
benzamide turns out to be too well hydrated for both charge 
 models with errors of 2.3 and 1.8 kcal / mol ( table 3 ) . in general , the 1.14*cm1a charges for amide nitrogens seem 
 large in magnitude at ca .
e with 1.27*cm5 and 0.76 and 0.50 e for 
 primary and secondary amides with opls - aa .
it is also noted that both 
 charge models predict poorer hydration of the e conformer 
 of nma by about 1.2 kcal / mol , while the available experimental data 
 indicate there is no e / z differential .
this discrepancy is a recurrent one going back 
 to the earliest fep calculations for amide e / z interconversions .
the experimental 
 measurements are challenging owing to the low population of the e conformer .
as an additional 
 check of the 
 reported free energies of hydration in table 3 , full molecular annihilations were performed for all molecules . 
 for molecules with up to 10 heavy atoms , sufficient convergence required 
 sampling roughly three - times the number of configurations for a typical 
 single heavy atom perturbation .
the free energy results from the sequential 
 and annihilation procedures with the 1.14*cm1a charges are compared 
 in figure 2 ; a similar plot for the 1.27*cm5 
 charges is shown in figure s2 .
excellent 
 correlations are observed for both cmx methods ; the 
 linear fits have slopes of 1.0 , intercepts near 0.0 , and r values of 0.995 .
the consistency confirms the precision 
 of the results in table 3 , and it also provides 
 validation of the annihilation methodology itself .
this permits more 
 automated calculations of free energies of hydration without the need 
 to devise a mutation sequence .
comparison of computed free energy of 
 hydration ( kcal / mol ) using 
 a series of fep calculations or annihilation with 1.14*cm1a charges . 

an additional 20 neutral , organic molecules 
 were studied by molecular annihilation to ascertain the validity and 
 transferability of the 1.27 scale factor .
molecules were chosen to 
 exhibit molecular diversity and for which independent free energies 
 of hydration have been previously computed .
both e and z isomers have been included for n - methylformamide , although no am1-bcc / gaff data are available 
 for this molecule .
the free energies of hydration are reported in 
 table 7 ; scaled cmx charges 
 are reported in table s7 .
the mue with 
 the 1.27*cm5 charges is 1.31 kcal / mol , while it is again higher , 1.47 
 kcal / mol , for the 1.14*cm1a charges .
am1-bcc / gaff has the lowest mue 
 for this set , though based on the error of 1.7 kcal / mol for n - methylacetamide in table 3 , inclusion 
 of results for nmf could increase the mue by ca .
the 
 results indicate that average errors of 1.01.5 kcal / mol can 
 be expected for application of these charge models to other small 
 molecules . for the 1.27*cm5 charges ,
aliphatic 
 amines are under - hydrated with all methods , while the performance 
 for amides in tables 3 and 7 is notably improved with the cmx charges .
the cumulative 
 errors for polypeptides can be expected to be large with many charge 
 models , which has implications for modeling protein stability and 
 folding .
results obtained from a fep annihilations ; 
 computed uncertainties are less than 0.25 kcal / mol .
a promising 
 attribute of charge model 5 is the ability to provide atomic charges 
 for any electronic structure method in conjunction with a hirshfeld 
 population analysis . for the present 
 context
, tests were performed to analyze the transferability of the 
 1.27 scale factor for alternative density functional methods .
specifically , 
 m06 , m06-l , b3lyp , and mpw1pw91 were utilized to derive cm5 charges for a subset of 10 
 molecules . the same procedure for obtaining the cm5 charges
was followed 
 as before , only the m06 - 2x method was replaced by the alternatives . 

absolute free energies of hydration were determined by charge perturbations 
 from 1.14*cm1a to the new 1.27*cm5 charges for each molecule in the 
 gas phase and in water .
the computed ghyd was added to the ghyd(1.14*cm1a ) for each molecule to determine the new ghyd(1.27*cm5 ) .
the final results are summarized 
 in table 8 including the standard deviation 
 for the five computed values for each molecule .
the effects of changing 
 the basis set on the ghyd results 
 were also examined with the m06 - 2x functional .
three additional basis 
 sets , 6 - 311g(d , p ) , 6 - 31+g(d , p ) , and 6 - 31g(d ) , were used to compute new 1.27*cm5 charges .
the absolute free energies 
 of hydration for the 10 molecules were again computed by charge perturbations . 

overall , little effect 
 is found on the computed free energies of 
 hydration from changes in the density functional method or basis set . 

the standard deviations average below 0.20 kcal / mol , which is near 
 the level of the statistical uncertainties in the results .
the conclusion 
 is that the scale factor of 1.27 for cm5 charges is valid for a wide 
 range of dft methods .
the 
 ease of access to cm5 charges from the gaussian 09 program coupled 
 with its implementation of continuum solvation models raised the possibility 
 of combining these methods to compute solvent - polarized charges .
such 
 charges might be appropriate for direct use in molecular mechanics 
 based fluid simulations .
single - point calculations were carried out 
 for the 42 molecules using m06 - 2x/6 - 311+g(2df,2p ) 
 and the conductor - like polarizable continuum model ( cpcm ) with the dielectric value for water , 78.3 .
the 
 hirshfeld charges were computed and processed with cm5pac to derive 
 new cm5 charges ( cm5/cpcm ) .
perturbations from the 1.14*cm1a to the 
 cm5/cpcm charges were then performed to obtain the ghyd values for the cm5/cpcm model .
the resultant 
 ghyd mue for the cm5/cpcm approach 
 is 2.11 kcal / mol .
this represents improvement from the mue of 3.08 
 kcal / mol with unscaled cm5 charges ; however , it is not competitive 
 with the mue of 1.10 kcal / mol using the 1.27*cm5 charges ( table 3 ) .
table s8 reports the 
 cm5/cpcm enhanced dipole moments and resultant free energies of hydration . 

cm5/cpcm dipole moments are significantly different from the hirshfeld / cpcm 
 dipole moments due to empirical adjustments by cm5 .
although the cm5/cpcm 
 dipole moments are enhanced by about 20% over cm5 and gas - phase experimental 
 values , this is insufficient for optimal modeling of chemistry in 
 aqueous solution with fixed - charge force fields .
since the average errors for free energies 
 of hydration with the 1.14*cm1a and 1.27*cm5 methods are similar and 
 near the 1 kcal / mol level , both approaches are reasonable for use 
 in simulations of aqueous systems .
a simple welch two - sample t test comparing cm1a and cm5 signed errors of the training 
 set produces a p - statistic of 0.328 and a t - statistic of 0.985 . while 
 no statistical significance can be made for the training set based 
 on this t test , correlation with experimental data 
 and precision
are improved with the 1.27*cm5 charges ( figure 1 , table s3 , figure s3 ) . a smaller standard deviation of unsigned errors for 1.27*cm5 versus 
 1.14*cm1a , 0.78 vs 0.89 kcal / mol , respectively , and a repeated reduced 
 mean unsigned error in the validation set , 1.31 vs 1.47 kcal / mol , 
 respectively , support this conclusion and highlight cm5 improvements 
 as important .
first , the cm1a method is we d to semiempirical 
 am1 wave functions , while the cm5 charges can be derived from hirshfeld 
 charges obtained from a wide variety of dft methods and basis sets .
the hirshfeld charges , cm5 charges , and , as 
 shown here , the resultant ghyd values 
 are insensitive to reasonable choices for the dft method and basis 
 set .
second , the variety of elements is limited with am1 , while the 
 cm5 model has been parametrized for all atoms of the periodic table .
third , the cm5 method yields more reasonable 
 charges for buried atoms , e.g. , amide nitrogen atoms as noted above , 
 and less dependence on conformation than alternative charge models .
finally , incorporation of cm5 charges into molecular 
 mechanics software is straightforward given access to gaussian 09 . 
 for boss , the subroutine that requests quantum mechanics calculations 

was modified to invoke an external call to a linker script , which 
 interfaces with gaussian .
the script ( i ) creates a gaussian input 
 file using solute coordinates and variables specifying the calculation 
 type from boss , ( ii ) initializes and executes a single - point calculation 
 in gaussian , and ( iii ) reads the output and loads the total energy 
 and cm5 charges back into boss .
though the present testing has only 
 considered a few elements , optimism can be expressed for broader utility 
 given the excellent performance of cm5 for dipole moments for a wide 
 range of molecules .
the recently reported cm5 charge model was tested for performance 
 in computing free energies of hydration in conjunction with the opls - aa 
 force field for the remaining force - field parameters .
an optimal scaling 
 factor of 1.27 for the cm5 charges was determined to minimize the 
 error in the computed free energies of hydration for 42 neutral organic 
 molecules .
the mean unsigned error of 1.10 kcal / mol from the 1.27*cm5 
 calculations compares favorably with the error of 1.17 kcal / mol from 
 the well - established 1.14*cm1a alternative .
both approaches give larger 
 errors for sulfur - containing molecules , and the 1.14*cm1a method makes 
 nitro groups much too polar .
additional attractive features of the 
 cm5 approach include the transferability of the 1.27 scale factor 
 to a wide range of density functional methods and basis sets , coverage 
 of all elements of the periodic table , and the availability of cm5 
 charges from the gaussian program .
use of the scaled cm5 charges in 
 conjunction with fixed - charge force fields should provide a viable 
 approach to modeling an enormous range of molecular systems in solution .
 the 
 recently developed charge model 5 ( cm5 ) is tested for its utility 
 in condensed - phase simulations . the cm5 approach , which derives partial 
 atomic charges from hirshfeld population analyses , provides excellent 
 results for gas - phase dipole moments and is applicable to all elements 
 of the periodic table . 
 herein , the adequacy of scaled cm5 charges 
 for use in modeling aqueous solutions has been evaluated by computing 
 free energies of hydration ( ghyd ) for 42 neutral organic molecules via monte carlo statistical mechanics . 
 
 an optimal scaling factor for the cm5 charges was determined to be 
 1.27 , resulting in a mean unsigned error ( mue ) of 1.1 kcal / mol for 
 the free energies of hydration . 
 testing for an additional 20 molecules 
 gave an mue of 1.3 kcal / mol . 
 the high precision of the results is 
 confirmed by free energy calculations using both sequential perturbations 
 and complete molecular annihilation . 
 performance for specific functional 
 groups is discussed ; sulfur - containing molecules yield the largest 
 errors . 
 in addition , the scaling factor of 1.27 is shown to be appropriate 
 for cm5 charges derived from a variety of density functional methods 
 and basis sets . 
 though the average errors from the 1.27*cm5 results 
 are only slightly lower than those using 1.14*cm1a charges , the broader 
 applicability and easier access to cm5 charges via the gaussian program 
 are additional attractive features . 
 the 1.27*cm5 charge model can 
 be used for an enormous variety of applications in conjunction with 
 many fixed - charge force fields and molecular modeling programs . 
Introduction
Computational Details
Results
Discussion
Conclusion