Approaching chemical accuracy with quantum Monte Carlo

A quantum Monte Carlo study of the atomization energies for the G2 set of molecules is presented. Basis size dependence of diffusion Monte Carlo atomization energies is studied with a single determinant Slater-Jastrow trial wavefunction formed from Hartree-Fock orbitals. With the largest basis set, the mean absolute deviation from experimental atomization energies for the G2 set is 3.0 kcal/mol. Optimizing the orbitals within variational Monte Carlo improves the agreement between diffusion Monte Carlo and experiment, reducing the mean absolute deviation to 2.1 kcal/mol. Moving beyond a single determinant Slater-Jastrow trial wavefunction, diffusion Monte Carlo with a small complete active space Slater-Jastrow trial wavefunction results in near chemical accuracy. In this case, the mean absolute deviation from experimental atomization energies is 1.2 kcal/mol. It is shown from calculations on systems containing phosphorus that the accuracy can be further improved by employing a larger active space.     

Accuracy of free energies of hydration for organic molecules from 6-31g*-derived partial charges

Absolute free energies of hydration have been computed for 13 diverse organic molecules using partial charges derived from ab initio 6-31G* wave functions. Both Mulliken charges and charges fit to the electrostatic potential surface (EPS) were considered in conjunction with OPLS Lennard–Jones parameters for the organic molecules and the TIP4P model of water. Monte Carlo simulations with statistical perturbation theory yielded relative free energies of hydration. These were converted to absolute quantities through perturbations to reference molecules for which absolute free energies of hydration had been obtained previously in TIP4P water. The average errors in the computed absolute free energies of hydration are 1.1 kcal/mol for the 6-31G* EPS charges and 4.0 kcal/mol for the Mulliken charges. For the EPS charges, the largest individual errors are under 2 kcal/mol except for acetamide, in which case the error is 3.7 kcal/mol. The hydrogen bonding between the organic solutes and water has also been characterized. © John Wiley & Sons, Inc.     

Solvent effect on K to Na ion mutation: a Monte Carlo simulation study

Monte Carlo simulation studies of statistical perturbation theory (SPT) have been carried out to investigate the solvent effects on the relative free energies of solvation and the difference in partition coefficients (log P) for K⁺ to Na⁺ ion mutation in the several solvents. We compared the relative free energies for interconversion of K⁺ to Na⁺, in H₂O (TIP4P) in this study with those published works, that in H₂O (TIP4P) is −16.55 kcal/mol in this study, those of the published works are −17.6, −17.3 and −17.31 kcal/mol and that of the experiment is −17.6 kcal/mol, respectively. Comparing the relative free energies for interconversion of K⁺ to Na⁺, in CH₃OH in this study with those published works, that in CH₃OH is −18.08±0.28 kcal/mol in this study, that of molecular dynamic simulation is −19.6±0.4 kcal/mol and that of the experimental work is −17.3 kcal/mol, respectively. There is good agreement among the several studies if we consider both methods of obtaining the solvation (or hydration) free energies and the standard deviations. For the present K⁺ and Na⁺ ions, the relative free energies of solvation vs Born's function of solvents are decreased with increasing Born's function of solvent except for CH₃OH, THF and MEOME. There is also good agreement between the calculated structural properties in this study and the computer simulation, ab initio and experimental works.     

Monte Carlo simulations of the hydration of substituted benzenes with OPLS potential functions

Intermolecular potential functions have been developed for use in computer simulations of substituted benzenes. Previously reported optimized potentials for liquid simulations (OPLS) for benzene and organic functional groups were merged and tested by computing free energies of hydration for toluene, p-xylene, phenol, anisole, benzonitrile, p-cresol, hydroquinone, and p-dicyanobenzene. The calculations featured Monte Carlo simulations at 25°C and 1 atm with statistical perturbation theory. The average difference between the computed results and experimental data for the absolute free energies of hydration is 0.5 kcal/mol. The AM1-SM2 method is also found to perform well in predicting the free energies of hydration for the substituted benzenes. In addition, the Monte Carlo simulations provided details on the hydration of the substituted benzenes, in particular for the solute–water hydrogen bonding. © 1993 John Wiley & Sons, Inc.     

Improved interaction potentials for charged residues in proteins

Electrostatic interactions dominate the structure and free energy of biomolecules. To obtain accurate free energies involving charged groups from molecular simulations, OPLS-AA parameters have been reoptimized using Monte Carlo free energy perturbation. New parameters fit a self-consistent, experimental set of hydration free energies for acetate (Asp), propionate (Glu), 4-methylimidazolium (Hip), n-butylammonium (Lys), and n-propylguanidinium (Arg), all resembling charged residue side chains, including beta-carbons. It is shown that OPLS-AA free energies depend critically on the type of water model, TIP4P or TIP3P; i.e., each water model requires specific water-charged molecule interaction potentials. New models (models 1 and 3) are thus described for both water models. Uncertainties in relative free energies of charged residues are approximately 2 kcal/mol with the new parameters, due to variations in system setup (MAEs of ca. 1 kcal/mol) and noise from simulations (ca. 1 kcal/mol). The latter error of approximately 1 kcal/mol contrasts MAEs from standard OPLS-AA of up to 13 kcal/mol for the entire series of charged residues or up to 5 kcal/mol for the cationic series Lys, Arg, and Hip. The new parameters can be used directly in molecular simulations with no modification of neutral residues needed and are envisioned to be particular important in simulations where charged residues change environment.     

Quantum Monte Carlo study of the reaction: Cl+CH3OH-->CH2OH+HCl

A theoretical study is reported of the Cl+CH3OH-->CH2OH+HCl reaction based on the diffusion Monte Carlo (DMC) variant of the quantum Monte Carlo method. Using a DMC trial function constructed as a product of Hartree-Fock and correlation functions, we have computed the barrier height, heat of reaction, atomization energies, and heats of formation of reagents and products. The DMC heat of reaction, atomization energies, and heats of formation are found to agree with experiment to within the error bounds of computation and experiment. M?ller-Plesset second order perturbation theory (MP2) and density functional theory, the latter in the B3LYP generalized gradient approximation, are found to overestimate the experimental heat of reaction. Intrinsic reaction coordinate calculations at the MP2 level of theory demonstrate that the reaction is predominantly direct, i.e., proceeds without formation of intermediates, which is consistent with a recent molecular beam experiment. The reaction barrier as determined from MP2 calculations is found to be 2.24 kcal/mol and by DMC it is computed to be 2.39(49) kcal/mol.     

Quantum monte carlo study of heats of formation and bond dissociation energies of small hydrocarbons

A quantum Monte Carlo (QMC) benchmark study of heats of formation at 298 K and bond dissociation energies (BDEs) of 22 small hydrocarbons is reported. Diffusion Monte Carlo (DMC) results, obtained using a simple product trial wavefunctions consisting of a single determinant and correlation function, are compared to experiment and to other theory including a version of complete basis set theory (CBS‐Q) and density functional theory (DFT) with the B3LYP functional. For heats of formation, the findings are a mean absolute deviation from experiment of 1.2 kcal/mol for CBS‐Q, 2.0 kcal/mol for B3LYP, and 2.2 kcal/mol for DMC. The mean absolute deviation of 31 BDEs is 2.0 kcal/mol for CBS‐Q, 4.2 kcal/mol for B3LYP, and 2.5 kcal/mol for DMC. These findings are for 17 BDEs of closed‐shell molecules that have mean absolute deviations from experiment of 1.7 kcal/mol (CBS‐Q), 4.0 kcal/mol (B3LYP), and 2.2 kcal/mol (DMC). The corresponding results for the 14 BDEs of open‐shell molecules studied are 2.4 kcal/mol (CBS‐Q), 4.3 kcal/mol (B3LYP), and 2.9 kcal/mol (DMC). The DMC results provide a baseline from which improvement using multideterminant trial functions can be measured. © 2005 Wiley Periodicals, Inc. Int J Chem Kinet 37: 583–592, 2005     

The accuracy of diffusion quantum Monte Carlo simulations in the determination of molecular equilibrium structures

For a test set of 17 first-row small molecules, the equilibrium structures are calculated with Ornstein-Uhlenbeck diffusion quantum Monte Carlo simulations guiding by trial wave functions constructed from floating spherical Gaussian orbitals and spherical Gaussian geminals. To measure performance of the Monte Carlo calculations, the mean deviation, the mean absolute deviation, the maximum absolute deviation, and the standard deviation of Monte Carlo calculated equilibrium structures with respect to empirical equilibrium structures are given. This approach is found to yield results having a uniformly high quality, being consistent with empirical equilibrium structures and surpassing calculated values from the coupled cluster model with single, double, and noniterative triple excitations [CCSD(T)] with the basis sets of cc-pCVQZ and cc-pVQZ. The nonrelativistic equilibrium atomization energies are also presented to assess performance of the calculated methods. The mean absolute deviations regarding experimental atomization energy are 0.16 and 0.21 kcal/mol for the Monte Carlo and CCSD(T)/cc-pCV(56)Z calculations, respectively.     

Toward the exact solution of the electronic Schrödinger equation for noncovalent molecular interactions: worldwide distributed quantum monte carlo calculations

Quantum Monte Carlo (QMC) calculations on the stacked (st) and Watson/Crick (wc) bound adenine/thymine (A/T) and cytosine/guanine (C/G) DNA base pair complexes were made possible with the first large scale distributed computing project in ab initio quantum chemistry, Quantum Monte Carlo at Home (QMC@HOME). The results for the interaction energies (wc-A/T = 15.7 kcal/mol, wc-C/G = 30.2 kcal/mol, st-A/T = 13.1 kcal/mol, st-C/G = 19.6 kcal/mol) are in very good agreement with the best known coupled-cluster based estimates. The accuracy of these values is further supported by calculations on the S22 benchmark set of noncovalently bound systems, for which we obtain a small mean absolute deviation of 0.68 kcal/mol. Our results support previous claims that the stacking energies are of comparable magnitude to the interactions of the commonly discussed hydrogen-bonded motif. Furthermore, we show that QMC can serve as an advantageous alternative to conventional wave function methods for large noncovalently bound systems. We also investigated in detail all technical parameters of the QMC simulations and recommend a careful optimization procedure of the Jastrow correlation factors in order to obtain numerically stable and reliable results.     

Bond dissocation and conformational energetics of tetrasulfur: a quantum Monte Carlo study

Variational Monte Carlo (VMC) and fixed-node diffusion Monte Carlo (DMC) calculations are performed for S4. The effect of single- and multireference trial functions, as well as choice of orbitals, is investigated for its effect on the quality of the Monte Carlo estimates. Estimates of symmetric (two S2 molecules) and asymmetric (S atom and S3 molecule) bond dissociation are reported. The conformational change of S4 from C2v to D2h defines a double-well potential and is also estimated. Multireference DMC with natural orbitals (DMC/NO) estimates the energy of the conformational change as 1.20(20) kcal/mol; the dissociation of the long S-S single bond is estimated at 21.1(1.3) kcal/mol, and the asymmetric bond energy is estimated as 53.2(2.4) kcal/mol. An estimate of the total atomization energy using multireference DMC/NO gives a value of 219.5(2.2) kcal/mol. The relative quality of result and implications for simplified trial function design are discussed.     

Theoretical study of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction by a diffusion quantum Monte Carlo approach

Ab initio calculations of transition state structure and reaction enthalpy of the F + H2-->HF + H reaction has been carried out by the fixed-node diffusion quantum Monte Carlo method in this study. The Monte Carlo sampling is based on the Ornstein-Uhlenbeck random walks guided by a trial wave function constructed from the floating spherical Gaussian orbitals and spherical Gaussian geminals. The Monte Carlo calculated barrier height of 1.09(16) kcal/mol is consistent with the experimental values, 0.86(10)/1.18(10) kcal/mol, and the calculated value from the multireference-type coupled-cluster (MRCC) calculation with the aug-cc-pVQZ(F)/cc-pVQZ(H) basis set, 1.11 kcal/mol. The Monte Carlo-based calculation also gives a similar value of the reaction enthalpy, -32.00(4) kcal/mol, compared with the experimental value, -32.06(17) kcal/mol, and the calculated value from a MRCC/aug-cc-pVQZ(F)/cc-pVQZ(H) calculation, -31.94 kcal/mol. This study clearly indicates a further application of the random-walk-based approach in the field of quantum chemical calculation.     

Breathing orbital valence bond method in diffusion Monte Carlo: C-H bond dissociation of acetylene

This study explores the use of breathing orbital valence bond (BOVB) trial wave functions for diffusion Monte Carlo (DMC). The approach is applied to the computation of the carbon-hydrogen (C-H) bond dissociation energy (BDE) of acetylene. DMC with BOVB trial wave functions yields a C-H BDE of 132.4 +/- 0.9 kcal/mol, which is in excellent accord with the recommended experimental value of 132.8 +/- 0.7 kcal/mol. These values are to be compared with DMC results obtained with single determinant trial wave functions, using Hartree-Fock orbitals (137.5 +/- 0.5 kcal/mol) and local spin density (LDA) Kohn-Sham orbitals (135.6 +/- 0.5 kcal/mol).     

Reliable radical stabilization energies from diffusion Monte Carlo calculations

We assess the performance of variational (VMC) and diffusion (DMC) quantum Monte Carlo methods for calculating the radical stabilization energies of a set of 43 carbon-centered radical species. Even using simple single-determinant trial wavefunctions, both methods perform exceptionally well, with mean absolute deviations from reference values well under the chemical accuracy standard of 1 kcal/mol. In addition, the use of DMC results in a highly concentrated spread of errors, with all 43 results within chemical accuracy at the 95% confidence level. These results indicate that DMC is an extremely reliable method for calculating radical stabilization energies and could be used as a benchmark method for larger systems in future.     

Reaction mechanism and tautomeric equilibrium of 2-mercaptopyrimidine in the gas phase and in aqueous solution: a combined Monte Carlo and quantum mechanics study

A combined Monte Carlo and quantum mechanical study was carried out to analyze the tautomeric equilibrium of 2-mercaptopyrimidine in the gas phase and in aqueous solution. Second- and fourth-order M?ller-Plesset perturbation theory calculations indicate that in the gas phase thiol (Pym-SH) is more stable than the thione (Pym-NH) by ca. 8 kcal/mol. In aqueous solution, thermodynamic perturbation theory implemented on a Monte Carlo NpT simulation indicates that both the differential enthalpy and Gibbs free energy favor the thione form. The calculated differential enthalpy is DeltaH(SH)(-->)(NH)(solv) = -1.7 kcal/mol and the differential Gibbs free energy is DeltaG(SH)(-->)(NH)(solv) = -1.9 kcal/mol. Analysis is made of the contribution of the solute-solvent hydrogen bonds and it is noted that the SH group in the thiol and NH group in the thione tautomers act exclusively as a hydrogen bond donor in aqueous solution. The proton transfer reaction between the tautomeric forms was also investigated in the gas phase and in aqueous solution. Two distinct mechanisms were considered: a direct intramolecular transfer and a water-assisted mechanism. In the gas phase, the intramolecular transfer leads to a large energy barrier of 34.4 kcal/mol, passing through a three-center transition state. The proton transfer with the assistance of one water molecule decreases the energy barrier to 17.2 kcal/mol. In solution, these calculated activation barriers are, respectively, 32.0 and 14.8 kcal/mol. The solvent effect is found to be sizable but it is considerably more important as a participant in the water-assisted mechanism than the solvent field of the solute-solvent interaction. Finally, the calculated total Gibbs free energy is used to estimate the equilibrium constant.     

Free energy calculations involving NH4+ in water

The analysis of the hydration of NH₄⁺ and the estimation of relative or absolute free energies of hydration by means of Monte Carlo computer simulations using different 1-6-12 potential functions is reported. Two electrostatic representations of NH₄⁺ (used respectively by W.L. Jorgensen and P.A. Kollman) in conjunction with two common water models (TIP3P and TIP4P) are considered. A change in relative hydration free energies of 1.7 kcal/mol is found when the NH₄⁺ models are mutated into each other in either TIP3P or TIP4P. The NH₄⁺ → Na⁺ mutation in both solvent models leads to similar but overestimated relative hydration energies of about ?28.7 kcal/mol. Similarly, the NH₄⁺ annihilation significantly overestimates the absolute free energy of hydration.     

The treatment of solvation by a generalized Born model and a self-consistent charge-density functional theory-based tight-binding method

We present a model to calculate the free energies of solvation of small organic compounds as well as large biomolecules. This model is based on a generalized Born (GB) model and a self-consistent charge-density functional theory-based tight-binding (SCC-DFTB) method with the nonelectrostatic contributions to the free energy of solvation modeled in terms of solvent-accessible surface areas (SA). The parametrization of the SCC-DFTB/GBSA model has been based on 60 neutral and six ionic molecules composed of H, C, N, O, and S, and spanning a wide range of chemical groups. Effective atomic radii as parameters have been obtained through Monte Carlo Simulated Annealing optimization in the parameter space to minimize the differences between the calculated and experimental free energies of solvation. The standard error in the free energies of solvation calculated by the final model is 1.11 kcal mol(-1). We also calculated the free energies of solvation for these molecules using a conductor-like screening model (COSMO) in combination with different levels of theory (AM1, SCC-DFTB, and B3LYP/6-31G*) and compared the results with SCC-DFTB/GBSA. To assess the efficiency of our model for large biomolecules, we calculated the free energy of solvation for a HIV protease-inhibitor complex containing 3,204 atoms using the SCC-DFTB/GBSA and the SCC-DFTB/COSMO models, separately. The computed relative free energies of solvation are comparable, while the SCC-DFTB/GBSA model is three to four times more efficient, in terms of computational cost.     

Heats of formation of triplet ethylene, ethylidene, and acetylene

Heats of formation of the lowest triplet state of ethylene and the ground triplet state of ethylidene have been predicted by high level electronic structure calculations. Total atomization energies obtained from coupled-cluster CCSD(T) energies extrapolated to the complete basis set limit using correlation consistent basis sets (CBS), plus additional corrections predict the following heats of formation in kcal/mol: DeltaH0r(C2H4,3A1) = 80.1 at 0 K and 78.5 at 298 K, and DeltaH0t(CH3CH,3A' ') = 86.8 at 0 K and 85.1 at 298 K, with an error of less than +/-1.0 kcal/mol. The vertical and adiabatic singlet-triplet separation energies of ethylene were calculated as DeltaES-T,vert = 104.1 and DeltaES-T,adia = 65.8 kcal/mol. These results are in excellent agreement with recent quantum Monte Carlo (DMC) values of 103.5 +/- 0.3 and 66.4 +/- 0.3 kcal/mol. Both sets of computational values differ from the experimental estimate of 58 +/- 3 kcal/mol for the adiabatic splitting. The computed singlet-triplet gap at 0 K for acetylene is DeltaES-T,adia(C2H2) = 90.5 kcal/mol, which is in notable disagreement with the experimental value of 82.6 kcal/mol. The heat of formation of the triplet is DeltaH0tC2H2,3B2) = 145.3 kcal/mol. There is a systematic underestimation of the singlet-triplet gaps in recent photodecomposition experiments by approximately 7 to 8 kcal/mol. For vinylidene, we predict DeltaH0t(H2CC,1A1) = 98.8 kcal/mol at 298 K (exptl. 100.3 +/- 4.0), DeltaH0t(H2CC,3B2) = 146.2 at 298 K, and an energy gap DeltaES-T-adia(H2CC) = 47.7 kcal/mol.     

Further development and validation of empirical scoring functions for structure-based binding affinity prediction

New empirical scoring functions have been developed to estimate the binding affinity of a given protein-ligand complex with known three-dimensional structure. These scoring functions include terms accounting for van der Waals interaction, hydrogen bonding, deformation penalty, and hydrophobic effect. A special feature is that three different algorithms have been implemented to calculate the hydrophobic effect term, which results in three parallel scoring functions. All three scoring functions are calibrated through multivariate regression analysis of a set of 200 protein-ligand complexes and they reproduce the binding free energies of the entire training set with standard deviations of 2.2 kcal/mol, 2.1 kcal/mol, and 2.0 kcal/mol, respectively. These three scoring functions are further combined into a consensus scoring function, X-CSCORE. When tested on an independent set of 30 protein-ligand complexes, X-CSCORE is able to predict their binding free energies with a standard deviation of 2.2 kcal/mol. The potential application of X-CSCORE to molecular docking is also investigated. Our results show that this consensus scoring function improves the docking accuracy considerably when compared to the conventional force field computation used for molecular docking.     

The lithium–thiophene interaction: a critical study using highly correlated electronic structure approaches of quantum chemistry

The fundamental multicentric interaction of a lithium atom with a single thiophene ring is addressed. A systematic study of the interaction energy (IE) and geometry for the Li–T charge-transfer complex is done at the MP2 and CCSD(T) levels using increasingly large basis sets up to aug-cc-pVQZ (AVQZ). Basis set superposition errors (BSSE) are evaluated and shown to have a major impact on the value of the IE. The Fixed-Node Diffusion Monte Carlo (FN-DMC) method is used as an alternative basis-set-free approach to obtain what is likely to be the most accurate estimate of the IE obtained so far. While counterpoise-corrected MP2/AVQZ and CCSD(T)/AVTZ interaction energies are found to be ?3.8 and ?7.5 kcal/mol, the FN-DMC method yields +1.3 ± 1.7 kcal/mol. The slow convergence of the ab initio IE (and some key structural parameters) with respect to basis set quality and the discrepancy with the FN-DMC result is discussed. A visualization of the electron pairing using the electron pair localization function (EPLF) for the Li-doped versus undoped thiophene is also presented.     

A computationally inexpensive modification of the point dipole electrostatic polarization model for molecular simulations

We present an approximation, which allows reduction of computational resources needed to explicitly incorporate electrostatic polarization into molecular simulations utilizing empirical force fields. The proposed method is employed to compute three-body energies of molecular complexes with dipolar electrostatic probes, gas-phase dimerization energies, and pure liquid properties for five systems that are important in biophysical and organic simulations-water, methanol, methylamine, methanethiol, and acetamide. In all the cases, the three-body energies agreed with high level ab initio data within 0.07 kcal/mol, dimerization energies-within 0.43 kcal/mol (except for the special case of the CH(3)SH), and computed heats of vaporization and densities differed from the experimental results by less than 2%. Moreover, because the presented method allows a significant reduction in computational cost, we were able to carry out the liquid-state calculations with Monte Carlo technique. Comparison with the full-scale point dipole method showed that the computational time was reduced by 3.5 to more than 20 times, depending on the system in hand and on the desired level of the full-scale model accuracy, while the difference in energetic results between the full-scale and the presented approximate model was not great in the most cases. Comparison with the nonpolarizable OPLS-AA force field for all the substances involved and with the polarizable POL3 and q90 models for water and methanol, respectively, demonstrates that the presented technique allows reduction of computational cost with no sacrifice of accuracy. We hope that the proposed method will be of benefit to research employing molecular modeling technique in the biophysical and physical organic chemistry areas.