An application of correlation energy density functionals to atoms and molecules

Four density functionals — including that recently introduced by Perdew ((1986) Phys Rev B33: 8822)—are tested for first-row atoms, hydrides and dimers. Calculated contributions of the correlation energy to the ionization potentials and electron affinities of atoms and to the dissociation energies of molecules are compared with empirical values which were reevaluated for this purpose. An improvement over Hartree-Fock is found in all cases if the self-interaction or the gradient correction are included in the density functional, although there is a rather large variation in the accuracy of the predictions.     

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Becke's original three-parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian-type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug-cc-pVTZ (UCC)]. The geometries and dipole moments of over 100 first-row and second-row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double-ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments. © 1997 by John Wiley & Sons, Inc.     

Behavior of density functionals with respect to basis set. VI. Truncation of the correlation consistent basis sets

Systematic truncation of the correlation consistent basis sets has been investigated in first and second row atoms and molecules to better understand basis set requirements for density functional theory, particularly the need for high angular momentum functions, as well as to understand possible computational cost savings that could be achieved by using reduced basis sets. The truncation scheme employed follows that recently introduced for ab initio methods [B. Mintz et al., J. Chem. Phys. 121, 5629 (2004)]. Properties examined in the current study include geometries, ionization potentials, electron affinities, and dissociation energies. In general, this investigation shows that a degree of truncation of higher angular momentum functions is possible with limited impact upon energetic properties, and does result in useful CPU time savings. However, not all properties investigated have the same level of dependence upon high angular momentum functions, and, thus, careful selection of truncated basis sets should be made.     

Paradigms and Paradoxes: Additive trends in the absolute entropy of monoxides and homonuclear diatomic molecules

Structural Chemistry - In general, entropy is not additive for the system of a single molecule. We show this by demonstrating that the entropy of a monoxide species, before and after subtracting...     

Full optimization of Jastrow-Slater wave functions with application to the first-row atoms and homonuclear diatomic molecules

We pursue the development and application of the recently introduced linear optimization method for determining the optimal linear and nonlinear parameters of Jastrow-Slater wave functions in a variational Monte Carlo framework. In this approach, the optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. We extend the method to optimize the exponents of the basis functions, simultaneously with all the other parameters, namely, the Jastrow, configuration state function, and orbital parameters. We show that the linear optimization method can be thought of as a so-called augmented Hessian approach, which helps explain the robustness of the method and permits us to extend it to minimize a linear combination of the energy and the energy variance. We apply the linear optimization method to obtain the complete ground-state potential energy curve of the C(2) molecule up to the dissociation limit and discuss size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations. We perform calculations for the first-row atoms and homonuclear diatomic molecules with fully optimized Jastrow-Slater wave functions, and we demonstrate that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems.     

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.     

Towards chemical accuracy for the thermodynamics of large molecules: new hybrid density functionals including non-local correlation effects

Two hybrid density functionals that include a second-order perturbation correction for non-local correlation effects are tested for the full G3/05 test set. Very large AO basis sets including core-polarization/correlation functions have been employed that yield for the first time results quite close to the basis set limit for this set. The B2-PLYP functional and the new mPW2-PLYP approach with a modified exchange part give by far the lowest MAD over the whole G3/05 set ever reported for a DFT method (2.5 and 2.1 kcal mol(-1), respectively). The big improvement compared to common density functionals is further demonstrated by the reduction of the maximum and minimum errors (outliers) and by much smaller errors for complicated molecular systems.     

Adiabatic and non-adiabatic corrections to rovibrational energies of diatomic molecules: variational calculations with experimental accuracy

Using the variational technique, eigensolutions of the radial Herman-Asgharian equation accounting for non-adiabatic terms are determined within the experimental accuracy of the high-resolution spectroscopy. This method, which is independent of the algebraic and numerical approaches currently used in the literature for a "direct-potential-fit" of diatomic rovibrational spectra, is shown to be useful for validation of available calculations and for resolving some controversial issues. Comparative discussions are reported in this paper for a dozen diatomic molecules.     

An analytic representation of the radial dependence of adiabatic and non-adiabatic corrections from molecular spectra of diatomic molecules

A method of determining the radial dependence of the adiabatic and non-adiabatic corrections contributing to the spectroscopie parameters Δ^a,b_kl of diatomic molecules according to an analytic representation is proposed. The method is applied to HCl and CO, and results for LiH are compared with published data.     

The decomposition of the SCF interaction energy in hydrogen bonded dimers corrected for basis set superposition errors: An examination of the basis set dependence

A systematic examination of the components of the interaction energy, obtained with the Kitaura and Morokuma method, for nine H-bonded dimers without and with counterpoise corrections (CP ) is presented. The nine dimers H_n A …? HBH_m correspond to all the possible combinations of HF, H₂O, and NH₃ as electron donors and electron acceptors. The interaction energy and the corresponding components have been computed over a sizable interval of intermolecular distances with five basis sets (STO -3G, MINI -1, 3-21G, 4-31G, 6-31G**) selected among those most extensively used to study interactions in larger systems. The CP corrections to the ΔE components have been obtained with a method, implemented in our group, which permits assignment to the pertinent components of ΔE of a physically reasonable portion of the CP correction even though different CP corrections are adopted. We examine here three versions of the CP correction, namely, the full CP correction (i.e., the original version of Boys and Bernardi) and CP corrections limited to the virtual space of the partner or to the electron donor only. The resulting data are employed to assess the basis set dependence of several models of hydrogen bonding (the electrostatic model, the semiclassical model, etc.) both with and without CP corrections.     

On the accuracy of frozen density embedding calculations with hybrid and orbital-dependent functionals for non-bonded interaction energies

We analyze the accuracy of the frozen density embedding (FDE) method, with hybrid and orbital-dependent exchange-correlation functionals, for the calculation of the total interaction energies of weakly interacting systems. Our investigation is motivated by the fact that these approaches require, in addition to the non-additive kinetic energy approximation, also approximate non-additive exact-exchange energies. Despite this further approximation, we find that the hybrid/orbital-dependent FDE approaches can reproduce the total energies with the same accuracy (about 1 mHa) as the one of conventional semi-local functionals. In many cases, thanks to error cancellation effects, hybrid/orbital-dependent approaches yield even the smallest error. A detailed energy-decomposition investigation is presented. Finally, the Becke-exchange functional is found to reproduce accurately the non-additive exact-exchange energies also for non-equilibrium geometries. These performances are rationalized in terms of a reduced-gradient decomposition of the non-additive exchange energy.     

Computational study of basis set and electron correlation effects on anapole magnetizabilities of chiral molecules

In the presence of a static, nonhomogeneous magnetic field, represented by the axial vector at the origin of the coordinate system and by the polar vector , assumed to be spatially uniform, the chiral molecules investigated in this paper carry an orbital electronic anapole, described by the polar vector . The electronic interaction energy of these molecules in nonordered media is a cross term, coupling and via , one third of the trace of the anapole magnetizability a_αβ tensor, that is, . Both and W^BC have opposite sign in the two enantiomeric forms, a fact quite remarkable from the conceptual point of view. The magnitude of predicted in the present computational investigation for five chiral molecules is very small and significantly biased by electron correlation contributions, estimated at the density functional level via three different functionals. © 2016 Wiley Periodicals, Inc.     

Study of the geometric structure of the molecules of H2O,Li2O,and LiOH by the method of diatomic fragments in molecules

Conclusion The results of the present work indicate that the DFM method can be used successfully to determine the geometric parameters of the ground states of triatomic molecules. The additional possibilities provided by the method are associated with the variation of the parameters of the theory which are not single-valued, in particular the parameters of the mixing of states of the same symmetry of the diatomic fragments. It has also been shown that the correct choice of the model of the molecule is of considerable importance.Chemistry Department, M. V. Lomonosov Moscow State University. Translated from Zhurnal Strukturnoi Khimii, Vol. 19, No. 5, pp. 771–778, September–October, 1978.     

An explicitly correlated local coupled cluster method for calculations of large molecules close to the basis set limit

A new explicitly correlated local coupled-cluster method with single and double excitations and a perturbative treatment of triple excitations [DF-LCCSD(T0)-F12x (x = a,b)] is presented. By means of truncating the virtual orbital space to pair-specific local domains (domain approximation) and a simplified treatment of close, weak and distant pairs using LMP2-F12 (pair approximation) the scaling of the computational cost with molecular size is strongly reduced. The basis set incompleteness errors as well as the errors due to the domain approximation are largely eliminated by the explicitly correlated terms. All integrals are computed using efficient density fitting (DF) approximations. The accuracy of the method is investigated for 52 reactions involving medium size molecules. A comparison of DF-LCCSD(T0)-F12x reaction energies with canonical CCSD(T)-F12x calculations shows that the errors introduced by the domain approximation are indeed very small. Care must be taken to keep the errors due to the additional pair approximation equally small, and appropriate distance criteria are recommended. Using these parameters, the root mean square (RMS) deviations of DF-LCCSD(T0)-F12a calculations with triple-ζ basis sets from estimated CCSD(T) complete basis set (CBS) limits and experimental data amount to only 1.5 kJ mol(-1) and 2.9 kJ mol(-1), respectively. For comparison, the RMS deviation of the CCSD(T)/CBS values from the experimental values amounts to 3.0 kJ mol(-1). The potential of the method is demonstrated for five reactions of biochemical or pharmacological interest which include molecules with up to 61 atoms. These calculations show that molecules of this size can now be treated routinely and yield results that are close to the CCSD(T) complete basis set limits.     

The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users. Contribution to the Mark S. Gordon 65th Birthday Festschrift Issue.     

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: a solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople's basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C-H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree-Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed.     

Adsorption of small aromatic molecules on gold: a DFT localized basis set study including van der Waals effects

Schrödinger equation for harmonium and related models may be transformed to the biconfluent Heun equation. The solubility of this equation and its applications in quantum chemistry are briefly discussed.