Parameterization of a B3LYP specific correction for non-covalent interactions and basis set superposition error on a gigantic dataset of CCSD(T) quality non-covalent interaction energies.

A vast number of non-covalent interaction energies at the counterpoise corrected CCSD(T) level have been collected from the literature to build a diverse new dataset. The whole dataset, which consists of 2027 CCSD(T) energies, includes most of the published data at this level. A large subset of the data was then used to train a novel, B3LYP specific, empirical correction scheme for non-covalent interactions and basis set superposition error (abbreviated as B3LYP-MM). Results obtained with our new correction scheme were directly compared to benchmark results obtained with B3LYP-D3(1) and M06-2X(2) (two popular density functions designed specifically to accurately model non-covalent interactions). For non-covalent complexes dominated by dispersion or dipole-dipole interactions all three tested methods give accurate results with the medium size aug-cc-pVDZ(3-6) basis set with MUE's of 0.27 (B3LYP-MM), 0.32 (B3LYP-D3) and 0.47 kcal/mol (M06-2X) (with explicit counterpoise corrections). These results validate both B3LYP-D3 and M06-2X for interactions of this type using a much larger data set than was presented in prior work. However, our new dispersion correction scheme shows some clear advantages for dispersion and dipole-dipole dominated complexes with the small LACVP* basis set, which is very popular in use due to its low associated computational cost: The MUE for B3LYP-MM with the LACVP* basis set for this subset of complexes (without explicit counterpoise corrections) is only 0.28 kcal/mol, compared to 0.65 kcal/mol for M06-2X or 1.16 kcal/mol for B3LYP-D3. Additionally, our new correction scheme also shows major improvements in accuracy for hydrogen-bonded systems and for systems involving ionic interactions, for example cation-π interactions. Compared to B3LYP-D3 and M06-2X, we also find that our new B3LYP-MM correction scheme gives results of higher or equal accuracy for a large dataset of conformer energies of di- and tripeptides, sugars, and cysteine.

Insights into the different dioxygen activation pathways of methane and toluene monooxygenase hydroxylases.

The methane and toluene monooxygenase hydroxylases (MMOH and TMOH, respectively) have almost identical active sites, yet the physical and chemical properties of their oxygenated intermediates, designated P*, H(peroxo), Q, and Q* in MMOH and ToMOH(peroxo) in a subclass of TMOH, ToMOH, are substantially different. We review and compare the structural differences in the vicinity of the active sites of these enzymes and discuss which changes could give rise to the different behavior of H(peroxo) and Q. In particular, analysis of multiple crystal structures reveals that T213 in MMOH and the analogous T201 in TMOH, located in the immediate vicinity of the active site, have different rotatory configurations. We study the rotational energy profiles of these threonine residues with the use of molecular mechanics (MM) and quantum mechanics/molecular mechanics (QM/MM) computational methods and put forward a hypothesis according to which T213 and T201 play an important role in the formation of different types of peroxodiiron(III) species in MMOH and ToMOH. The hypothesis is indirectly supported by the QM/MM calculations of the peroxodiiron(III) models of ToMOH and the theoretically computed Mössbauer spectra. It also helps explain the formation of two distinct peroxodiiron(III) species in the T201S mutant of ToMOH. Additionally, a role for the ToMOD regulatory protein, which is essential for intermediate formation and protein functioning in the ToMO system, is advanced. We find that the low quadrupole splitting parameter in the Mössbauer spectrum observed for a ToMOH(peroxo) intermediate can be explained by protonation of the peroxo moiety, possibly stabilized by the T201 residue. Finally, similarities between the oxygen activation mechanisms of the monooxygenases and cytochrome P450 are discussed.

Continuous Localized Orbital Corrections to Density Functional Theory: B3LYP-CLOC.

Our previous works have demonstrated the ability of our localized orbital correction (LOC) methodology to greatly improve the accuracy of various thermochemical properties at the stationary points of the Density Functional Theory (DFT) reaction coordinate (RC). Herein we extend this methodology from stationary points to the entire RC connecting any stationary points by developing continuous localized orbital corrections (CLOCs). We show that the resultant method, DFT-CLOC, is capable of producing RCs with far greater accuracy than uncorrected DFT and yet requires negligible computational cost beyond the uncorrected DFT calculations. Various post-Hartree-Fock (post-HF) reaction coordinate profiles were used, including a sigmatropic shift, Diels-Alder reaction, electrocyclization, carbon radical and three hydrogen radical reactions to show that this method is robust across multiple reaction types of general interest.

The prediction of Fe Mössbauer parameters by the density functional theory: a benchmark study.

We report the performance of eight density functionals (B3LYP, BPW91, OLYP, O3LYP, M06, M06-2X, PBE, and SVWN5) in two Gaussian basis sets (Wachters and Partridge-1 on iron atoms; cc-pVDZ on the rest of atoms) for the prediction of the isomer shift (IS) and the quadrupole splitting (QS) parameters of Mössbauer spectroscopy. Two sources of geometry (density functional theory-optimized and X-ray) are used. Our data set consists of 31 iron-containing compounds (35 signals), the Mössbauer spectra of which were determined at liquid helium temperature and where the X-ray geometries are known. Our results indicate that the larger and uncontracted Partridge-1 basis set produces slightly more accurate linear correlations of electronic density used for the prediction of IS and noticeably more accurate results for the QS parameter. We confirm and discuss the earlier observation of Noodleman and co-workers that different oxidation states of iron produce different IS calibration lines. The B3LYP and O3LYP functionals have the lowest errors for either IS or QS. BPW91, OLYP, PBE, and M06 have a mixed success whereas SVWN5 and M06-2X demonstrate the worst performance. Finally, our calibrations and conclusions regarding the best functional to compute the Mössbauer characteristics are applied to candidate structures for the peroxo and Q intermediates of the enzyme methane monooxygenase hydroxylase (MMOH), and compared to experimental data in the literature.

Localized orbital corrections for the calculation of barrier heights in density functional theory.

This work describes the extension of a previously reported empirical localized orbital correction model for density functional theory (DFT-LOC) for atomization energies, ionization potentials, electron affinities, and reaction enthalpies to the correction of barrier heights for chemical reactions of various types including cycloadditions, cycloreversions, dipolar cycloadditions, S(N)2's, carbon radical reactions, hydrogen radical reactions, sigmatropic shifts, and electrocyclizations. The B3LYP localized orbital correction version of the model (B3LYP-LOC) reduces the number of outliers and overall mean unsigned error (MUE) vs. experiment or ab initio values from 3.2 to 1.3 kcal/mole for barrier heights and from 5.1 to 1.1 kcal/mole for reaction enthalpies versus B3LYP. Furthermore, the new model has essentially zero additional computational cost beyond standard DFT calculations. Although the model is heuristic and is based on multiple linear regression to experimental or ab initio data, each of the parameters is justified on chemical grounds and provides insight into the fundamental limitations of DFT, most importantly the failure of current DFT methods to accurately account for nondynamical electron correlation.

Localized orbital corrections applied to thermochemical errors in density functional theory: The role of basis set and application to molecular reactions.

This paper is a logical continuation of the 22 parameter, localized orbital correction (LOC) methodology that we developed in previous papers [R. A. Friesner et al., J. Chem. Phys. 125, 124107 (2006); E. H. Knoll and R. A. Friesner, J. Phys. Chem. B 110, 18787 (2006).] This methodology allows one to redress systematic density functional theory (DFT) errors, rooted in DFT's inherent inability to accurately describe nondynamical correlation. Variants of the LOC scheme, in conjunction with B3LYP (denoted as B3LYP-LOC), were previously applied to enthalpies of formation, ionization potentials, and electron affinities and showed impressive reduction in the errors. In this paper, we demonstrate for the first time that the B3LYP-LOC scheme is robust across different basis sets [6-31G( *), 6-311++G(3df,3pd), cc-pVTZ, and aug-cc-pVTZ] and reaction types (atomization reactions and molecular reactions). For example, for a test set of 70 molecular reactions, the LOC scheme reduces their mean unsigned error from 4.7 kcal/mol [obtained with B3LYP/6-311++G(3df,3pd)] to 0.8 kcal/mol. We also verified whether the LOC methodology would be equally successful if applied to the promising M05-2X functional. We conclude that although M05-2X produces better reaction enthalpies than B3LYP, the LOC scheme does not combine nearly as successfully with M05-2X than with B3LYP. A brief analysis of another functional, M06-2X, reveals that it is more accurate than M05-2X but its combination with LOC still cannot compete in accuracy with B3LYP-LOC. Indeed, B3LYP-LOC remains the best method of computing reaction enthalpies.

The densities produced by the density functional theory: comparison to full configuration interaction.

We investigate one of the fundamental observables, electronic charge density, as produced by a number of popular functionals of the density functional theory (DFT): SVWN5, B3LYP, B3LYP, OLYP, O3LYP, BP86, B3P86, O3P86, and PBE using restricted and unrestricted orbitals. Measuring and comparing the quality of the densities could tell us more about the physical soundness of the functional models. The study is performed on the small molecules He, H2, LiH, H4 in an extensive range of correlation-consistent basis sets. We compare DFT densities to those of full configuration interaction (FCI) under the assumption that the FCI density in the largest employed basis set is sufficiently close to the exact one. For LiH and H4, we also compare the DFT densities to those of CCSD. The SVWN5 functional consistently shows the worst performance. The OPTX exchange functional regularly beats the Becke exchange. Among the best performers are all the hybrid functionals, the novel O3P86 being the most accurate in most cases. The popular functional B3LYP was consistently outmatched by O3LYP, and produced, in fact, some of the poorest densities among the hybrids. CCSD was found to produce much more accurate densities than any DFT functional in the case of LiH in equilibrium geometry, but was sometimes outperformed by DFT in the case of slightly stretched H4, where CCSD theory itself starts to break down. Surprisingly, as one stretches the H2 molecule, BP86 and PBE improve the description of density although such behavior is not observed in other systems. We conclude by reasoning how functionals such as B3LYP, despite being quite average for density, could still be very successful in predicting thermodynamic properties.

Hybrid correlation models based on active-space partitioning: seeking accurate O(N5) ab initio methods for bond breaking.

Moller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N5) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N5) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H2O, CH+, CH4, and Li2 molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N5) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.

Hybrid correlation models based on active-space partitioning: correcting second-order Moller-Plesset perturbation theory for bond-breaking reactions.

Moller-Plesset second-order (MP2) perturbation theory breaks down at molecular geometries which are far away from equilibrium. We decompose the MP2 energy into contributions from different orbital subspaces and show that the divergent behavior of the MP2 energy comes from the excitations located within a small (or sometimes even the minimal) active space. The divergent behavior of the MP2 energy at large interfragment distances may be corrected by replacing a small number of terms by their more robust counterparts from coupled-cluster (CCSD) theory. We investigated several schemes of such a substitution, and we find that a coupling between the active-space CCSD and the remaining MP2 amplitudes is necessary to obtain the best results. This naturally leads us to an approach which has previously been examined in the context of cost-saving approximations to CCSD for equilibrium properties by Nooijen [J. Chem. Phys. 111, 10815 (1999)]. The hybrid MP2-CCSD approach, which has the same formal scaling as conventional MP2 theory, provides potential curves with a correct shape for bond-breaking reactions of BH, CH(4), and HF. The error of the MP2-CCSD method (measured against full configuration-interaction data) is smaller than that of MP2 at all interfragment separations and is qualitatively similar to that of full CCSD.

A general diagrammatic algorithm for contraction and subsequent simplification of second-quantized expressions.

We present a general computer algorithm to contract an arbitrary number of second-quantized expressions and simplify the obtained analytical result. The functions that perform these operations are a part of the program Nostromo which facilitates the handling and analysis of the complicated mathematical formulas which are often encountered in modern quantum-chemical models. In contrast to existing codes of this kind, Nostromo is based solely on the Goldstone-diagrammatic representation of algebraic expressions in Fock space and has capabilities to work with operators as well as scalars. Each Goldstone diagram is internally represented by a line of text which is easy to interpret and transform. The calculation of matrix elements does not exploit Wick's theorem in a direct way, but uses diagrammatic techniques to produce only nonzero terms. The identification of equivalent expressions and their subsequent factorization in the final result is performed easily by analyzing the topological structure of the diagrammatic expressions.