Extension of the PDDG/PM3 and PDDG/MNDO semiempirical molecular orbital methods to the halogens

The new semiempirical methods, PDDG/PM3 and PDDG/MNDO, have been parameterized for halogens. For comparison, the original MNDO and PM3 were also reoptimized for the halogens using the same training set; these modified methods are referred to as MNDO' and PM3'. For 442 halogen-containing molecules, the smallest mean absolute error (MAE) in heats of formation is obtained with PDDG/PM3 (5.6 kcal/mol), followed by PM3' (6.1 kcal/mol), PDDG/MNDO (6.6 kcal/mol), PM3 (8.1 kcal/mol), MNDO' (8.5 kcal/mol), AM1 (11.1 kcal/mol), and MNDO (14.0 kcal/mol). For normal-valent halogen-containing molecules, the PDDG methods also provide improved heats of formation over MNDO/d. Hypervalent compounds were not included in the training set and improvements over the standard NDDO methods with sp basis sets were not obtained. For small haloalkanes, the PDDG methods yield more accurate heats of formation than are obtained from density functional theory (DFT) with the B3LYP and B3PW91 functionals using large basis sets. PDDG/PM3 and PM3' also give improved binding energies over the standard NDDO methods for complexes involving halide anions, and they are competitive with B3LYP/6-311++G(d,p) results including thermal corrections. Among the semiempirical methods studied, PDDG/PM3 also generates the best agreement with high-level ab initio G2 and CCSD(T) intrinsic activation energies for S(N)2 reactions involving methyl halides and halide anions. Finally, the MAEs in ionization potentials, dipole moments, and molecular geometries show that the parameter sets for the PDDG and reoptimized NDDO methods reduce the MAEs in heats of formation without compromising the other important QM observables.     

The limitations of Slater's element-dependent exchange functional from analytic density-functional theory

Our recent formulation of the analytic and variational Slater-Roothaan (SR) method, which uses Gaussian basis sets to variationally express the molecular orbitals, electron density, and the one-body effective potential of density-functional theory, is reviewed. Variational fitting can be extended to the resolution of identity method, where variationality then refers to the error in each two-electron integral and not to the total energy. However, a Taylor-series analysis shows that all analytic ab initio energies calculated with variational fits to two-electron integrals are stationary. It is proposed that the appropriate fitting functions be charge neutral and that all ab initio energies be evaluated using two-center fits of the two-electron integrals. The SR method has its root in Slater's Xalpha method and permits an arbitrary scaling of the Slater-Gàspàr-Kohn-Sham exchange-correlation potential around each atom in the system. The scaling factors are Slater's exchange parameters alpha. Of several ways of choosing these parameters, two most obvious are the Hartree-Fock (HF) alpha(HF) values and the exact atomic alpha(EA) values. The former are obtained by equating the self-consistent Xalpha energy and the HF energies, while the latter set reproduces exact atomic energies. In this work, we examine the performance of the SR method for predicting atomization energies, bond distances, and ionization potentials using the two sets of alpha parameters. The atomization energies are calculated for the extended G2 set of 148 molecules for different basis-set combinations. The mean error (ME) and mean absolute error (MAE) in atomization energies are about 25 and 33 kcal/mol, respectively, for the exact atomic alpha(EA) values. The HF values of exchange parameters alpha(HF) give somewhat better performance for the atomization energies with ME and MAE being about 15 and 26 kcal/mol, respectively. While both sets give performance better than the local-density approximation or the HF theory, the errors in atomization energy are larger than the target chemical accuracy. To further improve the performance of the SR method for atomization energies, a new set of alpha values is determined by minimizing the MAE in atomization energies of 148 molecules. This new set gives atomization energies half as large (MAE approximately 14.5 kcal/mol) and that are slightly better than those obtained by one of the most widely used generalized-gradient approximations. Further improvements in atomization energies require going beyond Slater's functional form for exchange employed in this work to allow exchange-correlation interactions between electrons of different spins. The MAE in ionization potentials of 49 atoms and molecules is about 0.5 eV and that in bond distances of 27 molecules is about 0.02 A. The overall good performance of the computationally efficient SR method using any reasonable set of alpha values makes it a promising method for study of large systems.     

Accurate interaction energies of hydrogen-bonded nucleic acid base pairs

Hydrogen-bonded nucleic acids base pairs substantially contribute to the structure and stability of nucleic acids. The study presents reference ab initio structures and interaction energies of selected base pairs with binding energies ranging from -5 to -47 kcal/mol. The molecular structures are obtained using the RI-MP2 (resolution of identity MP2) method with extended cc-pVTZ basis set of atomic orbitals. The RI-MP2 method provides results essentially identical with the standard MP2 method. The interaction energies are calculated using the Complete Basis Set (CBS) extrapolation at the RI-MP2 level. For some base pairs, Coupled-Cluster corrections with inclusion of noniterative triple contributions (CCSD(T)) are given. The calculations are compared with selected medium quality methods. The PW91 DFT functional with the 6-31G basis set matches well the RI-MP2/CBS absolute interaction energies and reproduces the relative values of base pairing energies with a maximum relative error of 2.6 kcal/mol when applied with Becke3LYP-optimized geometries. The Becke3LYP DFT functional underestimates the interaction energies by few kcal/mol with relative error of 2.2 kcal/mol. Very good performance of nonpolarizable Cornell et al. force field is confirmed and this indirectly supports the view that H-bonded base pairs are primarily stabilized by electrostatic interactions.     

Improved hybrid functional for solids: the HSEsol functional

We introduce the hybrid functional HSEsol. It is based on PBEsol, a revised Perdew-Burke-Ernzerhof functional, designed to yield accurate equilibrium properties for solids and their surfaces. We present lattice constants, bulk moduli, atomization energies, heats of formation, and band gaps for extended systems, as well as atomization energies for the molecular G2-1 test set. Compared to HSE, significant improvements are found for lattice constants and atomization energies of solids, but atomization energies of molecules are slightly worse than for HSE. Additionally, we present zero-point anharmonic expansion corrections to the lattice constants and bulk moduli, evaluated from ab initio phonon calculations.     

The computation of the potential energy surface for H2 + OH → H2O + H using ab initio and density functional theory methods

The reaction energy profile for H₂ + OH → H + H₂O was computed using HF, MP2, MP4, QCISD, G1, G2, and G2MP2 ab initio methods. In addition, the B3LYP, B3P86, B3PW91, BLYP, BP291, and SVWN density functional theory (DFT) methods were also used. All the ab initio methods, with the exception of the G series, produced much higher activation barriers and heats of reaction than the experimental values. On the other hand, the DFT methods produced negative forward and reverse barriers which were too low, with the exception of the hybrid DFT methods. The G2 ab initio method generated energies which deviated from the experimental values by ∼ 1 kcal/mol and therefore should be considered a very accurate computational method. The hybrid DFT methods produced positive forward reaction barriers with energies that were 2–4 kcal/mol lower than the experimental values. The geometries of the transition state and energies computed by the ab initio and DFT methods were compared. These results suggest that, in the hybrid exchange functional, the portion of the Slater exchange term should be increased. This may be the reason why the computed energies were too low. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 639–644, 1997     

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.     

Simple energy corrections for precise atomization energies of CHON molecules

We test a few ways to improve atomization energies of CHON molecules and found that the best way to do it is simply by correcting the atom energies of the participating atoms. Extraordinary improvement on the average errors is obtained. For the HF/6-31G** level of theory an average error of 271.2 kcal/mol on 115 molecules is improved to 6.7 kcal/mol simply by correcting the atomic energy of the four chon atoms. The corrections to density functional methods allow us to reach a chemical accuracy of 2 kcal/mol.     

Accurate energies calculated by empirical corrections to the local spin density approximation

We tested the efficacy of three empirical correction schemes on atomization energies calculated by the following theories: Kohn–Sham density functional theory (KS-DFT) with local spin density approximation (LSDA), two KS-DFT gradient-corrected methods, one hybrid Hartree–Fock/KS-DFT method similar to B3LYP, and the ab initio extrapolation procedures G1 and G2. Empirical corrections improved the LSDA results greatly, while the other theories were improved slightly or not at all. The best procedure for correcting LSDA atomization energies brings the mean absolute deviation from experiment from 38.3 to 4.0 kcal/mol on a subset of 44 molecules in the G1 dataset that were not used in deriving the empirical parameters. This corrected LSDA is interesting for three reasons: it could be a useful computational tool in some cases, it implies that the LSDA itself gives accurate energies for reactions where atomic coordinations stay unchanged, and it gives insight into the search of better functionals.     

Fast,efficient generation of high-quality atomic charges. AM1-BCC model: II. Parameterization and validation

We present the first global parameterization and validation of a novel charge model, called AM1-BCC, which quickly and efficiently generates high-quality atomic charges for computer simulations of organic molecules in polar media. The goal of the charge model is to produce atomic charges that emulate the HF/6-31G* electrostatic potential (ESP) of a molecule. Underlying electronic structure features, including formal charge and electron delocalization, are first captured by AM1 population charges; simple additive bond charge corrections (BCCs) are then applied to these AM1 atomic charges to produce the AM1-BCC charges. The parameterization of BCCs was carried out by fitting to the HF/6-31G* ESP of a training set of >2700 molecules. Most organic functional groups and their combinations were sampled, as well as an extensive variety of cyclic and fused bicyclic heteroaryl systems. The resulting BCC parameters allow the AM1-BCC charging scheme to handle virtually all types of organic compounds listed in The Merck Index and the NCI Database. Validation of the model was done through comparisons of hydrogen-bonded dimer energies and relative free energies of solvation using AM1-BCC charges in conjunction with the 1994 Cornell et al. forcefield for AMBER.(13) Homo- and hetero-dimer hydrogen-bond energies of a diverse set of organic molecules were reproduced to within 0.95 kcal/mol RMS deviation from the ab initio values, and for DNA dimers the energies were within 0.9 kcal/mol RMS deviation from ab initio values. The calculated relative free energies of solvation for a diverse set of monofunctional isosteres were reproduced to within 0.69 kcal/mol of experiment. In all these validation tests, AMBER with the AM1-BCC charge model maintained a correlation coefficient above 0.96. Thus, the parameters presented here for use with the AM1-BCC method present a fast, accurate, and robust alternative to HF/6-31G* ESP-fit charges for general use with the AMBER force field in computer simulations involving organic small molecules.     

Performance of multiplicity-based energy correctors for molecules containing second-row elements

We introduce a posteriori multiplicity-based corrections to ab initio energies in order to reproduce experimental atomization energies. This simple approach, as compared to the alternative ones to improve density functionals and standard correlated methods, requires less computational resources than higher levels of theory. We extend our approach to include molecules containing second-row elements. Molecules are taken from the Gaussian sets for which experimental values are known with errors of less than 1 kcal/mol. We postulate that inexpensive multiplicity-based corrections can account for effects that are not accounted because of the low level of theory of the method or because of the small basis used for the calculations.     

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.     

Accurate energetics of small molecules containing third-row atoms Ga-Kr: a comparison of advanced ab initio and density functional theory

Advanced ab initio [coupled cluster theory through quasiperturbative triple excitations (CCSD(T))] and density functional (B3LYP) computational chemistry approaches were used in combination with the standard and augmented correlation consistent polarized valence basis sets [cc-pVnZ and aug-cc-pVnZ, where n=D(2), T(3), Q(4), and 5] to investigate the energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 (G2) extended test set for third-row atoms. Several different schemes were used to extrapolate the calculated energies to the complete basis set (CBS) limit for CCSD(T) and the Kohn-Sham (KS) limit for B3LYP. Zero point energy and spin orbital corrections were included in the results. Overall, CCSD(T) atomization energies, ionization energies, proton affinities, and electron affinities are in good agreement with experiment, within 1.1 kcal/mol when the CBS limit has been determined using a series of two basis sets of at least triple zeta quality. For B3LYP, the overall mean absolute deviation from experiment for the three properties and the series of molecules is more significant at the KS limit, within 2.3 and 2.6 kcal/mol for the cc-pVnZ and aug-cc-pVnZ basis set series, respectively.     

Heats of formation of organic molecules by ab initio methods: Thiaalkanes

The bond energy scheme for calculating heats of formation of organic molecules from ab initio data (6–31G*) has been extended to include 24 compounds containing sulfur in the sulfide oxidation state. The rms deviation from the experimental values for these compounds is 0.54 kcal/mol, which is approximately experimental error.     

Ab initio and density functional theory study of the enthalpies of formation of F2SOx and FClSOx (x=1, 2)

Enthalpies of formation of F₂SO, F₂SO₂, FClSO and FClSO₂ molecules have been determined using ab initio molecular orbital theory and density functional theory (DFT) calculations. Different DFT approaches and levels of the Gaussian-3 and the complete basis set (CBS) ab initio model chemistries have been employed to calculate enthalpies of formation from both total atomization energies and isodesmic reaction schemes. The best values at 298 K for F₂SO, F₂SO₂, FClSO and FClSO₂ as derived from an average of G3, G3B3, CBS-Q and CBS-QB3 isodesmic energies are −140.6, −181.1, −92.6 and −132.3 kcal mol⁻¹, respectively. The results obtained suggest that the accumulated small component errors found in the DFT-based methods are significantly reduced at the ab initio levels employed. Structural properties, harmonic vibrational frequencies, mode assignations and infrared intensities derived from B3LYP and mPW1PW91 functional with the 6-311+G(3df) basis set are presented.     

Computations of 36 tautomer/isomer equilibria of different lactams

Gas-phase energies of 36 tautomer/isomer pairs of 18 six-membered N-heterocyclic compounds were computed quantum chemically. Among the considered B3LYP, BH&HLYP, BH&HLYP(G), and PW6B95 DFT functionals, the latter two provide accurate tautomer/isomer pair energies with root-mean-square deviations (rmsd) relative to experiments of 0.2 and 0.3 kcal/mol, respectively. Since only few (namely five) experimental data are available, 15 tautomer/isomer pair energies were computed with the very precise QCISD(T)(quadruple-ζ) method serving as reference. Relative to this reference the PW6B95 DFT functional is slightly superior to the BH&HLYP(G) functional, yielding an rmsd of 0.7 and 0.8 kcal/mol, respectively. In contrast to BH&HLYP(G), the PW6B95 DFT functional yields also accurate tautomer/isomer pair energies if zwitterionic structures are involved. The tautomer/isomer pair states possess different amounts of aromaticity. This is characterized by nucleus-independent chemical shift (NICS) values. The tautomer/isomer pair reference energies, from which the energies computed with PW6B95 are subtracted, correlate linearly with the corresponding differences in the NICS values. This correlation is used to construct a correction term for the pair energies computed with PW6B95, yielding tautomer/isomer pair energies with rmsd of 0.3 kcal/mol with respect to the more CPU time demanding QCISD(T)(quadruple-ζ) method.     

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.     

Ab initio, density functional theory, and continuum solvation model prediction of the product ratio in the S(N)2 reaction of NO2(-) with CH3CH2Cl and CH3CH2Br in DMSO solution

The reaction pathways for the interaction of the nitrite ion with ethyl chloride and ethyl bromide in DMSO solution were investigated at the ab initio level of theory, and the solvent effect was included through the polarizable continuum model. The performance of BLYP, GLYP, XLYP, OLYP, PBE0, B3PW91, B3LYP, and X3LYP density functionals has been tested. For the ethyl bromide case, our best ab initio calculations at the CCSD(T)/aug-cc-pVTZ level predicts product ratio of 73% and 27% for nitroethane and ethyl nitrite, respectively, which can be compared with the experimental values of 67% and 33%. This translates to an error in the relative DeltaG* of only 0.17 kcal mol(-1). No functional is accurate (deviation <0.5 kcal mol(-1)) for predicting relative DeltaG*. The hybrid X3LYP functional presents the best performance with deviation 0.82 kcal mol(-1). The present problem should be included in the test set used for the evaluation of new functionals.     

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.