Vibrational corrections to magneto-optical rotation: a computational study

Vibrational corrections to the Verdet constants of nine molecules (H2, N2, CO, H2O, CH4, benzene, toluene, p-xylene, and o-xylene) were calculated with pure density functional theory (DFT), hybrid DFT, and an approximate coupled-cluster theory. Comparisons are made for the accuracy of the vibrational averages among different methods and with respect to experimental data where available. It is found that vibrational corrections to magneto-optical rotation can be as large as 10% of the equilibrium value. Hybrid DFT with the B3LYP hybrid functional offers reasonable accuracy at a relatively inexpensive computational cost for accurate calculations of vibrationally averaged Verdet constants.     

A localized orbital analysis of the thermochemical errors in hybrid density functional theory: achieving chemical accuracy via a simple empirical correction scheme

This paper describes an empirical localized orbital correction model which improves the accuracy of density functional theory (DFT) methods for the prediction of thermochemical properties for molecules of first and second row elements. The B3LYP localized orbital correction version of the model improves B3LYP DFT atomization energy calculations on the G3 data set of 222 molecules from a mean absolute deviation (MAD) from experiment of 4.8 to 0.8 kcal/mol. The almost complete elimination of large outliers and the substantial reduction in MAD yield overall results comparable to the G3 wave-function-based method; furthermore, the new model has zero additional computational cost beyond standard DFT calculations. The following four classes of correction parameters are applied to a molecule based on standard valence bond assignments: corrections to atoms, corrections to individual bonds, corrections for neighboring bonds of a given bond, and radical environmental corrections. Although the model is heuristic and is based on a 22 parameter multiple linear regression to experimental errors, each of the parameters is justified on physical grounds, and each provides insight into the fundamental limitations of DFT, most importantly the failure of current DFT methods to accurately account for nondynamical electron correlation.     

Semiempirical evaluation of post-Hartree-Fock diagonal-Born-Oppenheimer corrections for organic molecules

Recent post-Hartree-Fock calculations of the diagonal-Born-Oppenheimer correction empirically show that it behaves quite similar to atomic nuclear mass corrections. An almost constant contribution per electron is identified, which converges with system size for specific series of organic molecules. This feature permits pocket-calculator evaluation of the corrections within thermochemical accuracy (10(-1) mhartree or kcal/mol).     

Leading-order relativistic effects on nuclear magnetic resonance shielding tensors

We present perturbational ab initio calculations of the nuclear-spin-dependent relativistic corrections to the nuclear magnetic resonance shielding tensors that constitute, together with the other relativistic terms reported by us earlier, the full leading-order perturbational set of results for the one-electron relativistic contributions to this observable, based on the (Breit-)Pauli Hamiltonian. These contributions are considered for the H(2)X (X = O,S,Se,Te,Po) and HX (X = F,Cl,Br,I,At) molecules, as well as the noble gas (Ne, Ar, Kr, Xe, Rn) atoms. The corrections are evaluated using the relativistic and magnetic operators as perturbations on an equal footing, calculated using analytical linear and quadratic response theory applied on top of a nonrelativistic reference state provided by self-consistent field calculations. The (1)H and heavy-atom nuclear magnetic shielding tensors are compared with four component, nearly basis-set-limit Dirac-Hartree-Fock calculations that include positronic excitations, as well as available literature data. Besides the easy interpretability of the different contributions in terms of familiar nonrelativistic concepts, the accuracy of the present perturbational scheme is striking for the isotropic part of the shielding tensor, for systems including elements up to Xe.     

Vibrational transitions of the 7LiH+ ion calculated without the Born-Oppenheimer approximation and with leading relativistic corrections

We recently presented very accurate calculations of the fundamental vibrational frequency of the (7)LiH(+) and (3)He(4)He(+) ions [Stanke et al. Phys. Rev. A 79, 060501(R) (2009)] performed without the Born-Oppenheimer approximation and included leading relativistic corrections. The accuracy of those calculations was estimated to be of the order of 0.06 cm(-1). In the present work we extend the calculations to the remaining pure vibrational states of (7)LiH(+) and similarly accurate results are generated. They may lead to the experimental search for still unidentified lines corresponding to those transitions.     

A study of factors affecting the accurac of combined calculation methods

By the example of combined calculation methods (CCMs) corresponding to calculations in MP4/6–311+G(fd,p)//MP2/6-31G(d,p) and MP4/aug-cc-pvTZ//MP2/cc-pvDZ approximations the factors affecting their accuracy are considered. By total energy calculations made for a number of compounds it is shown that the accuracy of CCMs reduces when valence double- and triple-split basis sets are applied together, and also when different methods are used to allow for electron correlation. The use of empirical corrections taking into account the character of the electron distribution in a molecule allows an enhancement of the accuracy of CCMs. The mentioned factors taken into account enable us to obtain CCM, for which the mean absolute deviation of calculation data is 1.0 kJ/mol and the largest maximum deviation is 8.0 kJ/mol in the total energy calculation in the MP4/6-311+G(f,d,p) approximation.     

Benchmark calculations of proton affinities and gas-phase basicities of molecules important in the study of biological phosphoryl transfer

Benchmark calculations of proton affinities and gas-phase basicities of molecules most relevant to biological phosphoryl transfer reactions are presented and compared with available experimental results. The accuracy of proton affinity and gas-phase basicity results obtained from several multi-level model chemistries (CBS-QB3, G3B3, and G3MP2B3) and density-functional quantum models (PBE0, B1B95, and B3LYP) are assessed and compared. From these data, a set of empirical bond enthalpy, entropy, and free energy corrections are introduced that considerably improve the accuracy and predictive capability of the methods. These corrections are applied to the prediction of proton affinity and gas-phase basicity values of important biological phosphates and phosphoranes for which experimental data does not currently exist. Comparison is made with results from semiempirical quantum models that are commonly employed in hybrid quantum mechanical/molecular mechanical simulations. Data suggest that the design of improved semiempirical quantum models with increased accuracy for relative proton affinity values is necessary to obtain quantitative accuracy for phosphoryl transfer reactions in solution, enzymes, and ribozymes.     

Calculation of molecular geometries,relative conformational energies,dipole moments,and molecular electrostatic potential fitted charges of small organic molecules of biochemical interest by density functional theory

Density functional theory is tested on a large ensemble of model compounds containing a wide variety of functional groups to understand better its ability to reproduce experimental molecular geometries, relative conformational energies, and dipole moments. We find that gradient-corrected density functional methods with triple-ζ plus polarization basis sets reproduce geometries well. Most bonds tend to be approximately 0.015 Å longer than the experimental results. Bond angles are very well reproduced and most often fall within a degree of experiment. Torsions are, on average, within 4 degrees of the experimental values. For relative conformational energies, comparisons with Hartree-Fock calculations and correlated conventional ab initio methods indicate that gradient-corrected density functionals easily surpass the Hartree-Fock approximation and give results which are nearly as accurate as MP2 calculations. For the 35 comparisons of conformational energies for which experimental data was available, the root mean square (rms) deviation for gradient-corrected functionals was approximately 0.5 kcal mol^?1. Without gradient corrections, the rms deviation is 0.8 kcal mol^?1, which is even less accurate than the Hartree-Fock calculations. Calculations with extended basis sets and with gradient corrections incorporated into the self-consistent procedure generate dipole moments with an rms deviation of 5%. Dipole moments from local density functional calculations, with more modest basis sets, can be scaled down to achieve roughly the same accuracy. In this study, all density functional geometries were generated by local density functional self-consistent calculations with gradient corrections added in a perturbative fashion. Such an approach generates results that are almost identical to the self-consistent gradient-corrected calculations, which require significantly more computer time. Timings on scalar and vector architectures indicate that, for moderately sized systems, our density functional implementation requires only slightly less computer resources than established Hartree-Fock programs. However, our density functional calculations scale much better and are significantly faster than their MP2 counterparts, whose results they approach. © 1995 John Wiley & Sons, Inc.     

Atomic energy levels from configuration interaction calculations with relativistic corrections

It is shown that configuration interaction calculations, with inclusion of the relativistic corrections, constitute an appropriate approach for the prediction of atomic energy levels and that results of experimental accuracy are possible given the availability of large-scale, fast computers. The results obtained for He through F emphasize both the practical difficulties to be encountered and the possibility of predictions with less than 1% error.     

Direct perturbation theory in terms of energy derivatives: fourth-order relativistic corrections at the Hartree-Fock level

In this work, the quantum-chemical treatment of relativistic effects by means of direct perturbation theory is extended from its lowest order, DPT2, to the next higher order, DPT4. The required theory is given in terms of energy derivatives with the DPT4 energy correction defined as the corresponding second derivative with respect to the relativistic perturbation parameter λ(rel) = c(2) and c as the speed of light. To facilitate the implementation in standard quantum-chemical program packages, a general formulation of DPT starting from a nonrelativistic Lagrangian is developed, thereby expanding both wave function and operators in terms of λ(rel). The corresponding expressions, which incorporate in an additive manner scalar-relativistic and spin-orbit contributions, are given at the Hartree-Fock level and have been implemented in the CFOUR program package using the available analytic second-derivative techniques. The accuracy of the DPT4 corrections at the HF level is investigated by comparison with rigorous four-component calculations. Scalar-relativistic and spin-orbit contributions are analyzed individually and the importance of the various terms to those corrections is discussed. Furthermore, the basis-set dependence of the computed DPT4 corrections is investigated.     

Counterpoise corrected interaction energies are not systematically better than uncorrected ones: comparison with CCSD(T) CBS extrapolated values

The effect of the inclusion of counterpoise corrections (CP) on the accuracy of interaction energies has been studied for different systems accounting for (1) intermolecular interactions, (2) intramolecular interactions and (3) chemical reactions. To minimize the error associated with the method of choice, the energy calculations were performed using CCSD(T) in all the cases. The values obtained using aug-cc-pVXZ basis sets are compared to CBS-extrapolated values. It has been concluded that at least for the tested systems CP corrections systematically leads to results that differ from the CBS-extrapolated ones to a larger extension than the uncorrected ones. Accordingly, from a practical point of view, we do not recommend the inclusion of such corrections in the calculation of interaction energies, except for CBS extrapolations. The best way of dealing with basis set superposition error (BSSE) is not to use CP corrections, but to make a computational effort for increasing the basis set. This approach does not eliminate BSSE but significantly decreases it, and more importantly it proportionally decreases all the errors arising from the basis set truncation.     

Quantitative prediction of gas-phase 19F nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via second-order vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are -1.9 and 1.6 ppm, respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Density-functional theory calculations of absolute and relative (19)F nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree-Fock self-consistent-field calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorine-oxygen, fluorine-nitrogen, and fluorine-fluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.     

Accurate Quantum‐Chemical Prediction of Enthalpies of Formation of Small Molecules in the Gas Phase

The coupled‐cluster approach, including single and double excitations and perturbative corrections for triple excitations, is capable of predicting molecular electronic energies and enthalpies of formation of small molecules in the gas phase with very high accuracy (specifically, with error bars less than 5 kJ mol^?1), provided that the electronic wavefunction is dominated by the Hartree–Fock configuration. This capability is illustrated by calculations on molecules containing O–H and O–F bonds, namely OH, FO, H₂O, HOF, and F₂O. To achieve this very high accuracy, it is imperative to account for electron‐correlation effects in a quantitative manner, either by using explicitly correlated two‐particle basis functions (R12 functions) or by extrapolating to the limit of a complete basis. Besides taking into account harmonic zero‐point vibrational energies, it is also necessary to account for anharmonic corrections to the zero‐point vibrational energies, to include the core orbitals into the coupled‐cluster calculations, and to account for spin–orbit corrections and scalar relativistic effects. These additional corrections constitute small but significant contributions in the range of 1–4 kJ mol^?1 to the enthalpies of formation of the aforementioned molecules. The highly accurate coupled‐cluster results, obtained by employing R12 functions and by including various corrections, are compared with standard Kohn–Sham density‐functional calculations as well as with the Gaussian‐2 and complete‐basis‐set model chemistries.     

A comparative assessment of the perturbative and renormalized coupled cluster theories with a noniterative treatment of triple excitations for thermochemical kinetics, including a study of basis set and core correlation effects

The CCSD, CCSD(T), and CR-CC(2,3) coupled cluster methods, combined with five triple-zeta basis sets, namely, MG3S, aug-cc-pVTZ, aug-cc-pV(T+d)Z, aug-cc-pCVTZ, and aug-cc-pCV(T+d)Z, are tested against the DBH24 database of diverse reaction barrier heights. The calculations confirm that the inclusion of connected triple excitations is essential to achieving high accuracy for thermochemical kinetics. They show that various noniterative ways of incorporating connected triple excitations in coupled cluster theory, including the CCSD(T) approach, the full CR-CC(2,3) method, and approximate variants of CR-CC(2,3) similar to the triples corrections of the CCSD(2) approaches, are all about equally accurate for describing the effects of connected triply excited clusters in studies of activation barriers. The effect of freezing core electrons on the results of the CCSD, CCSD(T), and CR-CC(2,3) calculations for barrier heights is also examined. It is demonstrated that to include core correlation most reliably, a basis set including functions that correlate the core and that can treat core-valence correlation is required. On the other hand, the frozen-core approximation using valence-optimized basis sets that lead to relatively small computational costs of CCSD(T) and CR-CC(2,3) calculations can achieve almost as high accuracy as the analogous fully correlated calculations.     

Density functional theory study of beta-hydride elimination of ethyl on flat and stepped Cu surfaces

Plane wave density functional theory calculations have been used to characterize the transition states for beta-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programmed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions.     

Demonstrating why DFT-calculations for molecular transport in solvents need scissor corrections

With the aid of two typical molecules [(4, 4′)-bipyridine and octanedithiol], often used to fabricate nanoelectronic devices, we demonstrate why DFT calculations for the transport in single-molecule junctions immersed in solvents are not only quantitatively but also qualitatively inappropriate, (ii) why, in order to obtain meaningful results, scissor corrections are needed, and (iii) that scissor corrections can be deduced by quantum chemical calculations that can obviate the explicit treatment the atomistic structure of the solvent.     

Predicting adsorption enthalpies on silicalite and HZSM‐5: A benchmark study on DFT strategies addressing dispersion interactions

We evaluated the accuracy of periodic density functional calculations for adsorption enthalpies of water, alkanes, and alcohols in silicalite and HZSM‐5 zeolites using a gradient‐corrected density functional with empirical dispersion corrections (PBE‐D) as well as a nonlocal correlation functional (vdW‐DF2). Results of both approaches agree in acceptable fashion with experimental adsorption energies of alcohols in silicalite, but the adsorption energies for n‐alkanes in both zeolite models are overestimated, by 21?46 kJ mol^?1. For PBE‐D calculations, the adsorption of alkanes is exclusively determined by the empirical dispersion term, while the generalized gradient approximation‐DFT part is purely repulsive, preventing the molecule to come too close to the zeolite walls. The vdW‐DF2 results are comparable to those of PBE‐D calculations, but the latter values are slightly closer to the experiment in most cases. Thus, both computational approaches are unable to reproduce available experimental adsorption energies of alkanes in silicalite and HZSM‐5 zeolite with chemical accuracy. © 2014 Wiley Periodicals, Inc.     

Cost reduction of high-order coupled-cluster methods via active-space and orbital transformation techniques

We discuss several techniques which have the potential to decrease the computational expenses of high-order coupled-cluster (CC) methods with a reasonable loss in accuracy. In particular, the CC singles, doubles, and triples (CCSDT) as well as the CC singles, doubles, triples, and perturbative quadruples [CCSDT(Q)] methods are considered, which are frequently used in high-precision model chemistries for the calculation of iterative triples and quadruples corrections. First, we study the possibilities for using active spaces to decrease the computational costs. In this case, an active space is defined and some indices of cluster amplitudes are restricted to be in the space. Second, the application of transformed virtual orbitals is investigated. In this framework, to reduce the computation time the dimension of the properly transformed virtual one-particle space is truncated. We have found that the orbital transformation techniques outperform the active-space approaches. Using the transformation techniques, the computational time can be reduced in average by an order of magnitude without significant loss in accuracy. It is demonstrated that high-order CC calculations are possible for considerably larger systems than before using the implemented techniques.