Energy correctors for accurate prediction of molecular energies

Energy correctors are introduced for the calculation of molecular energies of compounds containing first row atoms (Li-F) to modify ab initio molecular orbital calculations of energies to better reproduce experimental results. Four additive correctors are introduced to compensate for the differences in the treatment of molecules with different spin multiplicities and multiplicative correctors are also calculated for the electronic and zero-point vibrational energies. These correctors, individually and collectively yield striking improvements in the atomization energies for several ab initio methods. We use as training set the first row subset of molecules from the G1 basis of molecules; when the correctors are applied to other molecules not included in the training set, selected from the G3 basis, similar improvements in the atomization energies are obtained. The special case of the B3PW91/cc-pVTZ yields an average error of 1.2 kcal/mol, which is already within a chemical accuracy and comparable to the Gaussian-n theories accuracy. The very inexpensive B3PW91/6-31G** yields an average error of 2.1 kcal/mol using the correctors. Methods considered unsuitable for energetics such as HF and LSDA yield corrected energies comparable to those obtained with the best highly correlated methods.     

A fast empirical GAFF compatible partial atomic charge assignment scheme for modeling interactions of small molecules with biomolecular targets

We report here a new and fast approach [Transferable Partial Atomic Charge Model (TPACM4)-upto four bonds] for deriving the partial atomic charges of small molecules for use in protein/DNA-ligand docking and scoring. We have created a look-up table of 5302 atom types to cover the chemical space of C, H, O, N, S, P, F, Cl, and Br atoms in small molecules together with their quantum mechanical RESP fit charges. The atom types defined span diverse plausible chemical environments of each atom in a molecule. The partial charge on any atom in a given molecule is then assigned by a reference to the look-up table. We tested the sensitivity of the TPACM4 partial charges in estimates of hydrogen bond dimers energies, solvation free energies and protein-ligand binding free energies. An average error ±1.11 kcal/mol and a correlation coefficient of 0.90 is obtained in the calculated protein-ligand binding free energies vis-à-vis an RMS error of ±1.02 kcal/mol and a correlation coefficient of 0.92 obtained with RESP fit charges in comparison to experiment. Similar accuracies are realized in predictions of hydrogen bond energies and solvation free energies of small molecules. For a molecule containing 50-55 atoms, the method takes on the order of milliseconds on a single processor machine to assign partial atomic charges. The TPACM4 programme has been web-enabled and made freely accessible at http://www.scfbio-iitd.res.in/software/drugdesign/charge.jsp.     

Fitting atomic correlation parameters for RECEP (rapid estimation of correlation energy from partial charges) method to estimate molecular correlation energies within chemical accuracy

The accuracy of the RECEP method [Chem Phys 1997, 224, 33 and Chem Phys Lett 1999, 307, 469] has been increased considerably by the use of fitted atomic correlation parameters. This method allows an extremely rapid, practically prompt calculation of the correlation energy of molecules after an HF‐SCF calculation. The G2 level correlation energy and HF‐SCF charge distribution of 41 closed‐shell neutral molecules (composed of H, C, N, O, and F atoms) of the G2 thermochemistry database were used to obtain the fitted RECEP atomic correlation parameters. Four different mathematical definitions of partial charges, as a multiple choice, were used to calculate the molecular correlation energies. The best results were obtained using the natural population analysis, although the other three are also recommended for use. For the 41 molecules, the G2 results were approached within a 1.8 kcal/mol standard deviation (the mean absolute difference was 1.5 kcal/mol). The RECEP atomic correlation parameters were also tested on a different, nonoverlapping set of other 24 molecules from the G2 thermochemistry database. The G2 results of these 24 molecules were approached within a 2.3 kcal/mol standard deviation (the mean absolute difference was 1.9 kcal/mol). This method is recommended to estimate total correlation energies of closed shell ground‐state neutral molecules at stationary (minimums and transition states) points on the potential surface. Extension of the work for charged molecules, radicals, and molecules containing other atoms is straightforward. Numerical example as a recipe is also provided. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 241–254, 2001     

Besides N(2), What Is the Most Stable Molecule Composed Only of Nitrogen Atoms?

Polynitrogen molecules have been studied systematically at high levels of ab initio and density functional theory (DFT). Besides N(2), the thermodynamically most stable N(n)() molecules, located with the help of a newly developed energy increment system, are all based on pentazole units. The geometric, energetic, and magnetic criteria establish pentazole (2) and its anion (3) to be as aromatic as their isoelectronic analogues, e.g., furan, pyrrole, and the cyclopentadienyl anion. The bond lengths in 2 and 3 are equalized; both have large aromatic stabilization energies (ASE) and also substantial magnetic susceptibility exaltations (Lambda). The C(s)() symmetric azidopentazole (14), a candidate for experimental investigation, is the lowest energy N(8) isomer but is still 196.7 kcal/mol higher in energy than four N(2) molecules. Octaazapentalene (12) with 10 pi electrons also is aromatic. The D(2)(d)() symmetric bispentazole (21) is the lowest energy N(10) minimum but is 260 kcal/mol higher in energy than five N(2) molecules. For strain-free molecules, the average deviation is +/-2.6 kcal/mol between the DFT energies and those based on the increment scheme. The increment scheme also provides estimates of the strain energies of polynitrogen compounds, e.g., tetraazatetrahedrane (8, 48.2 kcal/mol), octaazacubane (11, 192.6 kcal/mol), and N(20) (27, 294.6 kcal/mol), and is useful in searching for new high-energy-high-density materials.     

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.     

Multiple bonds and excited states from the Hartree-Fock-Heitler-London method

The recently proposed Hartree-Fock-Heitler-London, HF-HL, method (Corongiu, G. J. Phys. Chem. A 2006, 110, 11584) previously tested for single bond molecules is validated by potential energy computations for open and closed shells, single and multiple bonds, in ground and excited states of homopolar diatomic molecules of the first and second period. The simple HF-HL function, including the configurations for 2s/2p near degeneracy and avoiding state crossing, yields correct dissociation products, qualitatively correct binding, and accounts for non-dynamical correlation. Addition of ionic structures improves the ab initio HF-HL function and yields about 95% of the experimental binding energies on average. Computed excitation energies are also in agreement with laboratory values as verified for the 3 Pi u and 3 Zeta g- excited states of the C2 molecule. Computation of the remaining dynamical correlation using a semiempirical functional yields binding energies with an average deviation of 1.5 kcal/mol from laboratory values, and total energies with an average deviation of 0.7 kcal/mol from exact nonrelativistic dissociation energies.     

Gaussian-4 theory

The Gaussian-4 theory (G4 theory) for the calculation of energies of compounds containing first- (Li-F), second- (Na-Cl), and third-row main group (K, Ca, and Ga-Kr) atoms is presented. This theoretical procedure is the fourth in the Gaussian-n series of quantum chemical methods based on a sequence of single point energy calculations. The G4 theory modifies the Gaussian-3 (G3) theory in five ways. First, an extrapolation procedure is used to obtain the Hartree-Fock limit for inclusion in the total energy calculation. Second, the d-polarization sets are increased to 3d on the first-row atoms and to 4d on the second-row atoms, with reoptimization of the exponents for the latter. Third, the QCISD(T) method is replaced by the CCSD(T) method for the highest level of correlation treatment. Fourth, optimized geometries and zero-point energies are obtained with the B3LYP density functional. Fifth, two new higher level corrections are added to account for deficiencies in the energy calculations. The new method is assessed on the 454 experimental energies in the G305 test set [L. A. Curtiss, P. C. Redfern, and K. Raghavachari, J. Chem. Phys. 123, 124107 (2005)], and the average absolute deviation from experiment shows significant improvement from 1.13 kcal/mol (G3 theory) to 0.83 kcal/mol (G4 theory). The largest improvement is found for 79 nonhydrogen systems (2.10 kcal/mol for G3 versus 1.13 kcal/mol for G4). The contributions of the new features to this improvement are analyzed and the performance on different types of energies is discussed.     

Implementation of pseudopotential in the G3 theory for molecules containing first-, second-, and non-transition third-row atoms

Compact effective pseudopotential (CEP) is adapted in the G3 theory providing a theoretical alternative referred to as G3CEP for calculations involving the first-, second-, and non-transition third-row elements. These modifications tried to preserve as much as possible the original characteristics of G3. G3CEP was used in the study of 247 enthalpies of formation, 22 atomization energies, 104 ionization potentials, 63 electron affinities, and 10 proton affinities, resulting in the calculation of 446 species for the first-, second-, and third-row atoms. The final average total absolute deviation was of 1.29 kcal mol(-1) against 1.16 kcal mol(-1) from all-electron G3 for the same calculations. The CPU time has been reduced by 7% to 56%, depending on the size of the molecules and the type of atoms considered.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

Optimized Slater-type basis sets for the elements 1-118

Seven different types of Slater type basis sets for the elements H (Z = 1) up to E118 (Z = 118), ranging from a double zeta valence quality up to a quadruple zeta valence quality, are tested in their performance in neutral atomic and diatomic oxide calculations. The exponents of the Slater type functions are optimized for the use in (scalar relativistic) zeroth-order regular approximated (ZORA) equations. Atomic tests reveal that, on average, the absolute basis set error of 0.03 kcal/mol in the density functional calculation of the valence spinor energies of the neutral atoms with the largest all electron basis set of quadruple zeta quality is lower than the average absolute difference of 0.16 kcal/mol in these valence spinor energies if one compares the results of ZORA equation with those of the fully relativistic Dirac equation. This average absolute basis set error increases to about 1 kcal/mol for the all electron basis sets of triple zeta valence quality, and to approximately 4 kcal/mol for the all electron basis sets of double zeta quality. The molecular tests reveal that, on average, the calculated atomization energies of 118 neutral diatomic oxides MO, where the nuclear charge Z of M ranges from Z = 1-118, with the all electron basis sets of triple zeta quality with two polarization functions added are within 1-2 kcal/mol of the benchmark results with the much larger all electron basis sets, which are of quadruple zeta valence quality with four polarization functions added. The accuracy is reduced to about 4-5 kcal/mol if only one polarization function is used in the triple zeta basis sets, and further reduced to approximately 20 kcal/mol if the all electron basis sets of double zeta quality are used. The inclusion of g-type STOs to the large benchmark basis sets had an effect of less than 1 kcal/mol in the calculation of the atomization energies of the group 2 and group 14 diatomic oxides. The basis sets that are optimized for calculations using the frozen core approximation (frozen core basis sets) have a restricted basis set in the core region compared to the all electron basis sets. On average, the use of these frozen core basis sets give atomic basis set errors that are approximately twice as large as the corresponding all electron basis set errors and molecular atomization energies that are close to the corresponding all electron results. Only if spin-orbit coupling is included in the frozen core calculations larger errors are found, especially for the heavier elements, due to the additional approximation that is made that the basis functions are orthogonalized on scalar relativistic core orbitals.     

Probing the bent bonds in cyclopropane systems for gas storage and separation process: A computational study

The hydrogen, carbon dioxide, and carbon monoxide gas adsorption and storage capacity of lithium-decorated cyclopropane ring systems were examined with quantum chemical calculations at density functional theory, DFT M06-2X functional using 6-31G(d) and cc-pVDZ basis sets. To examine the reliability of M06-2X DFT functional, a few representative systems are also examined with complete basis set CBS-QB3 method and CCSD-aug-cc-pVTZ level of theory. The cyclopropane systems can bind to one Li⁺ ion; however, the corresponding the methylated systems can bind with two Li⁺ ions. The cyclopropane systems can adsorb six hydrogen molecules with an average binding energy of 3.8 kcal/mol. The binding free energy (ΔG) values suggest that the hydrogen adsorption process is feasible at 273.15 K. The calculation of desorption energies indicates the recyclable property of gas adsorbed complexes. The same number of CO₂ and CO gas molecules can also be adsorbed with an average binding energy of −14.4 kcal/mol and −10.7 kcal/mol, respectively. The carbon dioxide showed ~3–4 kcal/mol better binding energy as compared to carbon monoxide and hence such designed systems can function as a potential candidate for the separation of these flue gas molecules. The nature of interactions in complexes was examined with atoms in molecules analysis revealed the electrostatic nature for the interaction of Li⁺ ion with cyclopropane rings. The chemical hardness and electrophilicity calculations showed that the gas adsorbed complexes are rigid and therefore robust as gas storage materials.     

Visualizing internal stabilization in weakly bound systems using atomic energies: hydrogen bonding in small water clusters

Atomic energies are used to visualize the local stabilizing and destabilizing energy changes in water clusters. Small clusters, (H(2)O)(n), from n = 2-5, at MP2/aug-cc-pVTZ geometries are evaluated using energies defined by the quantum theory of atoms in molecules (QTAIM). The atomic energies reproduce MP2 total energies to within 0.005 kcal mol(-1). Oxygen atoms are stabilized for all systems and hydrogen atoms are destabilized. The increased stability of the water clusters due to hydrogen bond cooperativity is demonstrated at an atomic level. Variations in atomic energies within the clusters are correlated to the geometry of the waters and reveal variations in the hydrogen bond strengths. The method of visualization of the energy changes applied here is especially suited for application to large biomolecules.     

A new database and benchmark of the bond energies of noble-gas-containing molecules

We have developed a new database of structures and bond energies of 59 noble-gas-containing molecules. The structures were calculated by CCSD(T)/aug-cc-pVTZ methods and the bond energies were obtained using the CCSD(T)/complete basis set method. Many wavefunction-based and density functional theory methods have been benchmarked against the 59 accurate bond energies. Our results show that the MPW1B95, B2GP-PLYP, and DSD-BLYP functionals with the aug-cc-pVTZ basis set excel in predicting the bond energies of noble-gas molecules with mean unsigned errors (MUEs) of 2.0 to 2.1 kcal/mol. When combinations of Dunning's basis sets are used, the MPW1B95, B2GP-PLYP, DSD-BLYP, and BMK functionals give significantly lower MUEs of 1.6 to 1.9 kcal/mol. Doubly hybrid methods using B2GP-PLYP and DSD-BLYP functionals and MP2 calculation also provide satisfactory accuracy with MUEs of 1.4 to 1.5 kcal/mol. If the Ng bond energies and the total atomization energies of a group of 109 main-group molecules are considered at the same time, the MPW1B95/aug-cc-pVTZ single-level method (MUE = 2.7 kcal/mol) and the B2GP-PLYP and DSD-PLYP functionals with combinations of basis sets or using the doubly hybrid method (MUEs = 1.9-2.2 kcal/mol) give the overall best result.     

The 6-31B(d) basis set and the BMC-QCISD and BMC-CCSD multicoefficient correlation methods

Three new multicoefficient correlation methods (MCCMs) called BMC-QCISD, BMC-CCSD, and BMC-CCSD-C are optimized against 274 data that include atomization energies, electron affinities, ionization potentials, and reaction barrier heights. A new basis set called 6-31B(d) is developed and used as part of the new methods. BMC-QCISD has mean unsigned errors in calculating atomization energies per bond and barrier heights of 0.49 and 0.80 kcal/mol, respectively. BMC-CCSD has mean unsigned errors of 0.42 and 0.71 kcal/mol for the same two quantities. BMC-CCSD-C is an equally effective variant of BMC-CCSD that employs Cartesian rather than spherical harmonic basis sets. The mean unsigned error of BMC-CCSD or BMC-CCSD-C for atomization energies, barrier heights, ionization potentials, and electron affinities is 22% lower than G3SX(MP2) at an order of magnitude less cost for gradients for molecules with 9-13 atoms, and it scales better (N6 vs N,7 where N is the number of atoms) when the size of the molecule is increased.     

Calculation of solvation free energies of charged solutes using mixed cluster/continuum models

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H(+) and 2.0 kcal/mol for Cu(2+). Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H(+) and >30 kcal/mol for Cu(2+). The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancellation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H(+) (6 waters) and 27 kcal/mol for Cu(2+) (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu(2+) (18 waters) and 1 kcal/mol for H(+) (10 waters).     

ESCAPE: A novel approach for a fast estimation of dynamic correlation energies: Application to large organic molecules

Advanced wave function-based quantum chemical ab initio methods, such as CCSD(T), are able to calculate the energies of small- to medium-sized molecules with chemical accuracy. Unfortunately, these methods scale quite unfavorably with the size of the system and are getting too time consuming—and too expensive—for larger molecules. In order to be able to treat larger organic molecules, we propose a novel scheme for a quick and reliable estimate of molecular correlation energies, which we call ESCAPE (ES timation of C orrelA tion energies by P air E nergies). It is based on the pair correlation energies for localized molecular orbitals that have been generated by CCSD[T] and fitted to suitable functional forms. All fit parameters are stored in a large parameter file. Aiming at chemical accuracy (±1 kcal/mol), we have first limited our approach to aliphatic hydrocarbons. The total molecular CCSD[T] correlation energies of a training set of 41 aliphatic hydrocarbons could be reproduced with a mean absolute error (MAE) of 0.56 kcal/mol or 0.11%. A similar accuracy could be obtained for a test set of 11 additional hydrocarbons with up to eight carbon atoms (MAE of 0.65 kcal/mol or 0.09%). In a more critical test, we checked the small energy differences for a set of 13 isomerization reactions. The comparison with experimental data showed that we could reach chemical accuracy as well. Our estimate (MAE of 0.55 kcal/mol) is slightly inferior to the CCSD[T] result (MAE of 0.17 kcal/mol), but superior to SCF, DFT/B3LYP, and DFT/B3LYP + D3. Moreover, in all cases, we obtained the correct sign, that is, the correct equilibrium structure. A similar accuracy could be reached in an application to the three lowest isomers of the C₆₀ molecule. Using the example of a set of eight alcohols, we were able to proof the method's ability for molecules including heteroatoms. Three fast steps are necessary for the application to any aliphatic hydrocarbon or alcohol: (1) An SCF calculation at the selected molecular geometry; it can be fast since a medium size basis set is generally sufficient. (2) The localization of the occupied molecular orbitals and determination of their properties (center of charge and spatial extent). (3) Estimate of the correlation energy using the existing parameter file. © 2019 Wiley Periodicals, Inc.     

Assessment of Gaussian-3 and density-functional theories on the G3/05 test set of experimental energies

The G3/99 test set [L. A. Curtiss, K. Raghavachari, P. C. Redfern, and J. A. Pople, J. Chem. Phys. 112, 7374 (2000)] of thermochemical data for validation of quantum chemical methods is expanded to include 78 additional energies including 14 enthalpies of formation of the first- and second-row nonhydrogen molecules, 58 energies of molecules containing the third-row elements K, Ca, and Ga-Kr, and 6 hydrogen-bonded complexes. The criterion used for selecting the additional systems is the same as before, i.e., experimental uncertainties less than +/- 1 kcal/mol. This new set, referred to as the G3/05 test set, has a total of 454 energies. The G3 and G3X theories are found to have mean absolute deviations of 1.13 and 1.01 kcal/mol, respectively, when applied to the G3/05 test set. Both methods have larger errors for the nonhydrogen subset of 79 species for which they have mean absolute deviations of 2.10 and 1.64 kcal/mol, respectively. On all of the other types of energies the G3 and G3X methods are very reliable. The G3/05 test set is also used to assess density-functional methods including a series of new functionals. The most accurate functional for the G3/05 test set is B98 with a mean absolute deviation of 3.33 kcal/mol, compared to 4.14 kcal/mol for B3LYP. The latter functional has especially large errors for larger molecules with a mean absolute deviation of 9 kcal/mol for molecules having 28 or more valence electrons. For smaller molecules B3LYP does as well or better than B98 and the other functionals. It is found that many of the density-functional methods have significant errors for the larger molecules in the test set.     

Estimation of intramolecular hydrogen bond energy via molecular tailoring approach

A novel method, based on the molecular tailoring approach for estimating intramolecular hydrogen bond energies, is proposed. Here, as a case study, the O-H...O bond energy is directly estimated by addition/subtraction of the single point individual fragment energies. This method is tested on polyhydroxy molecules at MP2 and B3LYP levels of theory. It is seen to be able to distinguish between weak ( approximately 1 kcal mol(-1)) and moderately strong ( approximately 5 kcal mol(-1)) hydrogen bonds in polyhydroxy molecules.     

Predicting binding affinities of host-guest systems in the SAMPL3 blind challenge: the performance of relative free energy calculations

Relative free energy calculations based on molecular dynamics simulations are combined with available experimental binding free energies to predict unknown binding affinities of acyclic Cucurbituril complexes in the blind SAMPL3 competition. The predictions yield root mean square errors between 2.6 and 3.2 kcal/mol for seven host-guest systems. Those deviations are comparable to results for solvation free energies of small organic molecules. However, the standard deviations found in our simulations range from 0.4 to 2.4 kcal/mol, which indicates the need for better sampling. Three different approaches are compared. Bennett's Acceptance Ratio Method and thermodynamic integration based on the trapezoidal rule with 12 λ-points exhibit a root mean square error of 2.6 kcal/mol, while thermodynamic integration with Simpson's rule and 11 λ-points leads to a root mean square error of 3.2 kcal/mol. In terms of absolute median errors, Bennett's Acceptance Ratio Method performs better than thermodynamic integration with the trapezoidal rule (1.7 vs. 2.9 kcal/mol). Simulations of the deprotonated forms of the guest molecules exhibit a poorer correspondence to experimental results with a root mean square error of 5.2 kcal/mol. In addition, a decrease of the buffer concentration by approximately 20 mM in the simulations raises the root mean square error to 3.8 kcal/mol.     

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.