Exchange–correlation potentials and local energies per particle along nonlinear adiabatic connections

We study nonlinear adiabatic connection paths in density-functional theory using modified electron–electron interactions that perform a long-range/short-range separation of the Coulomb interaction. These adiabatic connections allow us to define short-range exchange–correlation potentials and short-range local exchange–correlation energies per particle which we have calculated accurately for the He and Be atoms and compared to the corresponding quantities in the local density approximation (LDA). The results confirm that the LDA better describes exchange–correlation potentials and local exchange–correlation energies per particle when the range of the interaction is reduced.     

Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations

The random-phase approximation (RPA) for the electron correlation energy, combined with the exact-exchange (EX) energy, represents the state-of-the-art exchange-correlation functional within density-functional theory. However, the standard RPA practice--evaluating both the EX and the RPA correlation energies using Kohn-Sham (KS) orbitals from local or semilocal exchange-correlation functionals--leads to a systematic underbinding of molecules and solids. Here we demonstrate that this behavior can be corrected by adding a "single excitation" contribution, so far not included in the standard RPA scheme. A similar improvement can also be achieved by replacing the non-self-consistent EX total energy by the corresponding self-consistent Hartree-Fock total energy, while retaining the RPA correlation energy evaluated using KS orbitals. Both schemes achieve chemical accuracy for a standard benchmark set of noncovalent intermolecular interactions.     

Calculation of accurate imaginary frequencies and tunnelling coefficients for hydrogen abstraction reactions using IRCmax

The effect of level of theory on the imaginary frequency and corresponding tunnelling coefficients has been studied for a test set of hydrogen abstraction reactions: ?CH₂X + CH₃Y → CH₃X + ?CH₂Y for (X,Y) = (H,H), (H,CN), (H,F), (H,Li) and (F,Li). It is found that the imaginary frequency is very sensitive to the level of theory used, with Hartree-Fock (HF) methods severely overestimating the imaginary frequency compared with high-level CCSD(T)/6-311G(d,p) calculations. The errors for the other methods are smaller but nonetheless significant, with MP2 methods overestimating the imaginary frequency and density functional theory (DFT) methods underestimating it. In the case of the HF methods, this leads to errors in the tunnelling coefficient of several orders of magnitude, while for the better DFT and MP2 methods errors of a factor of 2–3 are observed. To address this problem, an IRCmax procedure for estimating the imaginary frequency has been developed and it is found that IRCmax imaginary frequencies calculated with CCSD(T)/6-311G(d,p) single points along a low-level HF/6-31G(d) minimum energy path provide excellent approximations to the high-level values, at a fraction of the computational cost.     

Anatomy of molecular properties evaluated with explicitly correlated electronic wave functions

Static electric dipole and quadrupole moments were evaluated at the explicitly correlated second-order Møller–Plesset (MP2-F12) level for BH, CO, H₂O, and HF molecules. The electron correlation contributions to the multipole moments were further decomposed into the direct (unrelaxed) and indirect (orbital response) components; we found that both components are equally important for the conventional (MP2) contribution, whereas the F12 correction to these properties originates primarily from the orbital response effects. Finally, the direct contribution dominates in the perturbative Hartree–Fock basis set incompleteness (CABS singles) correction. Two basis set families were employed: the standard aug-cc-pVXZ series and the cc-pVXZ-F12 series designed specifically for the F12 methods. The aug-cc-pVXZ MP2-F12 multipole moments usually have smaller basis set errors than the cc-pVXZ-F12 counterparts, albeit their differences are small at the triple (X = T) and quadruple (X = Q) zeta level. With the MP2-F12 calculations, the basis set errors of dipole and quadrupole moments can be reduced to ～0.001 a.u., or roughly 0.1%, at the aug-cc-pVDZ and aug-cc-pVTZ levels, respectively.     

Efficient band gap prediction for solids

An efficient method for the prediction of fundamental band gaps in solids using density functional theory (DFT) is proposed. Generalizing the Delta self-consistent-field (ΔSCF) method to infinite solids, the Δ-sol method is based on total-energy differences and derived from dielectric screening properties of electrons. Using local and semilocal exchange-correlation functionals (local density and generalized gradient approximations), we demonstrate a 70% reduction of mean absolute errors compared to Kohn-Sham gaps on over 100?compounds with experimental gaps of 0.5-4?eV, at computational costs similar to typical DFT calculations.     

Comparison of Theoretical Methods and Basis Sets for ab initio and DFT Calculations of the Structure and Frequencies of Normal Vibrations of Polyatomic Molecules

The dependence of the quality of calculation of the geometric parameters and frequencies of normal vibrations on the choice of the theoretical method and the basis set of Gaussian functions has been investigated within the framework of four approximations (DFT/B3LYP, HF, MP2, MP3), using benzene and s-triazine molecules as an example. It has been shown that the molecular parameters calculated using the basis set without polarization functions within the framework of any of the above theoretical methods agree poorly with the experimental data. It has been concluded that the use of the basis set 6-31G(d) within the framework of these methods with allowance for the electron correlation for calculating the geometric parameters and frequencies of normal vibrations of polyatomic cyclic compounds is most optimum in terms of the relation between the expenditure of time and the quality of the calculation. The coefficients of linear scaling of frequencies have been obtained by the DFT/B3LYP method for 22 basis sets that were tested on porphin, pyrrole, indene, and pyridine molecules. Atypically large errors in determining the frequencies of some benzene and s-triazine vibrations have been obtained in a number of quantum-mechanical calculations with large basis sets. The changes in the force field for these cases have been investigated with the example of the benzene molecule.     

氘代甲烷几何构型及物性的量子化学研究

用HF/6-31G^**、密度泛函方法B3LYP/31G^**、二级微扰MP2/6-31G^**、四级微扰MP4/6-31G^**方法对甲烷和氘代甲烷进行几何构型全优化,并将优化的结果与实验值进行比较.用上述4种方法对甲烷和氘代甲烷分子进行分子的振动基频计算.密度泛函、二级微扰、四级微扰优于HF/6-31G^**,尤其是密度泛函、四级微扰方法.密度泛函方法所用的机时远小于微扰方法.不同方法计算所得的氘代甲烷振动频率值与实验值的最大误差为10.4%,最小误差为2.0%.     

Optical saturation driven by exciton confinement in molecular chains: a time-dependent density-functional theory approach

We identify excitonic confinement in one-dimensional molecular chains (i.e., polyacetylene and H2) as the main driving force for the saturation of the chain polarizability as a function of the number of molecular units. This conclusion is based on first principles time-dependent density-functional theory calculations using a recently developed exchange-correlation kernel that accounts for excitonic effects. The failure of simple local and semilocal functionals is shown to be linked to the lack of memory effects, spatial ultranonlocality, and self-interaction corrections. These effects get smaller as the gap reduces, in which case such simple approximations do perform better.     

Quantum-chemical calculations of the structure,vibrational spectra,and torsional and inversion potentials of methylcarbamate

We present results of ab initio and DFT calculations of the structure, potential functions of the methyl group internal rotation and the amino group inversion, and vibrational frequencies and intensities in IR and Raman spectra of methylcarbamate. The calculations were carried out using different basis sets in the HF, MP2, and DFT/B3LYP approximations. The influence of both the basis set size and the allowance for electronic correlation on peculiarities of the structure of the amino group in methylcarbamate has been analyzed. It is shown that the B3LYP/6-311++G(2d, p) and B3LYP/cc-pVDZ calculations reproduce highly accurately experimental geometric parameters of methylcarbamate. Parameters of torsional and inversion potentials and characteristics of vibrational spectra calculated in different approximations show satisfactory agreement with experimental values. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 76, No. 3, pp. 349–357, May–June, 2009.     

Wavefunction stability analysis without analytical electronic Hessians: application to orbital-optimised second-order Møller–Plesset theory and VV10-containing density functionals

Wavefunction stability analysis is commonly applied to converged self-consistent field (SCF) solutions to verify whether the electronic energy is a local minimum with respect to second-order variations in the orbitals. By iterative diagonalisation, the procedure calculates the lowest eigenvalue of the stability matrix or electronic Hessian. However, analytical expressions for the electronic Hessian are unavailable for most advanced post-Hartree–Fock (HF) wave function methods and even some Kohn–Sham (KS) density functionals. To address such cases, we formulate the Hessian-vector product within the iterative diagonalisation procedure as a finite difference of the electronic gradient with respect to orbital perturbations in the direction of the vector. As a model application, following the lowest eigenvalue of the orbital-optimised second-order Møller–Plesset perturbation theory (OOMP2) Hessian during H₂ dissociation reveals the surprising stability of the spin-restricted solution at all separations, with a second independent unrestricted solution. We show that a single stable solution can be recovered by using the regularised OOMP2 method (δ-OOMP2), which contains a level shift. Internal and external stability analyses are also performed for SCF solutions of a recently developed range-separated hybrid density functional, ωB97X-V, for which the analytical Hessian is not yet available due to the complexity of its long-range non-local VV10 correlation functional.     

Chlorination of ammonia and aliphatic amines by Cl2: DFT study of medium and substituent effects

The mechanism of chlorination of ammonia and aliphatic amines by Cl₂ was studied by quantum‐chemical calculations using a series of DFT functionals. Three different reaction pathways were considered for the reaction between Cl₂ and NH₃ in the gas phase. Several intermediates and transition state structures, not described earlier, were located on the corresponding potential energy surface. It is calculated that the reaction field effects (SCIPCM) on the chlorination is much less pronounced than the effect of a specific solvent interaction which was modeled by an explicit water molecule. It is also found that the calculated energy barrier and the reaction free energy of the chlorination of different amines are dependent on the alkyl‐substituent effects. With increase in the basicity of amine, the chlorination reaction becomes more feasible. Calculated geometries of intermediates and overall reaction energetics are significantly influenced by the method for a treatment of electron correlation (DFT vs. MP2), and by the fraction of HF exchange (χ) in DFT functionals. With increase in the χ in the corresponding functional, the DFT results approach those obtained at the MP2 level, and are closer to experimental values, as well. Copyright © 2008 John Wiley & Sons, Ltd.     

Quantum chemical analysis of vibrational spectra of methylphenylcarbamate

We present results of ab initio and DFT calculations of the structure, potential function of internal rotation of the methyl group, and vibrational frequencies and intensities in IR and Raman spectra of methylphenylcarbamate. The calculations were carried out in different basis sets in the HF, MP2, and DFT/B3LYP approximations with partial force field scaling. The influence of the phenyl substituent on structural and spectral characteristics of the urethane group has been analyzed. Calculated characteristics of vibrational spectra show satisfactory agreement with experimental values.     

Electron correlation and the stability of substituted alkenes

Isomerization energies for hexenes (C₆H₁₂) were evaluated with ab initio (Hartree–Fock (HF), MP2, SCS‐MP2, and CCSD(T)) and several density functional approximation (DFA) methods. CCSD(T)/6‐311+G(2d,p) energies were taken as a benchmark standard. The HF method incorrectly predicts that monosubstituted alkenes are more stable than multiply‐substituted alkenes. DFAs generally predict the correct stability trends of alkenes (mono‐, < di‐, < tri‐, < tetra‐substituted alkenes) but errors in popular functionals, such as B3LYP, can be as large as errors found for alkane hydrocarbon thermochemistries. Some of the HF error is traced back to deficiencies in modeling 1,3‐geminal and 1,4‐vicinal alkyl–alkyl group interactions, called vinylbranches, and changes in C? C and C? H bond types (sp³–sp² C? C to sp³–sp³ C? C and sp³ C? H to sp² C? H). The latter is shown to be more significant. Comparison of CCSD(T) energies of trans‐2‐butene with 2‐methylpropylene and cis‐2‐butene suggests that geminal vinylbranches are stabilizing while vicinal vinylbranches are destabilizing. B3LYP and other DFAs have much smaller errors than HF theory due to inclusion of correlation energy that better reproduces bond type changes. Copyright © 2011 John Wiley & Sons, Ltd.     

Exploring weight-dependent density-functional approximations for ensembles in the Hubbard dimer

Gross–Oliveira–Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excited-state densities. The ensemble energy (i.e. the weighted sum of ground- and excited-state energies) can be obtained variationally as a functional of the ensemble density. Like in DFT, the key ingredient to model in GOK-DFT is the exchange-correlation functional. Developing density-functional approximations (DFAs) for ensembles is a complicated task as both density and weight dependencies should in principle be reproduced. In a recent paper [K. Deur et al., Phys. Rev. B 95, 035120 (2017)], the authors applied exact GOK-DFT to the simple but nontrivial Hubbard dimer in order to investigate (numerically) the importance of weight dependence in the calculation of excitation energies. In this work, we derive analytical DFAs for various density and correlation regimes by means of a Legendre–Fenchel transform formalism. Both functional and density driven errors are evaluated for each DFA. Interestingly, when the ensemble exact-exchange-only functional is used, these errors can be large, in particular if the dimer is symmetric, but they cancel each other so that the excitation energies obtained by linear interpolation are always accurate, even in the strongly correlated regime.     

An accurate theory for the square-well potential: from long to short well width

Density function theory (DFT) is combined with the first-order mean spherical approximation (FMSA) to study the radial distribution function (RDF) of the square-well (SW) potential. The combination (DFT + FMSA) is based on the direct correlation function (DCF) of the FMSA. Upon comparison with computer simulation data, DFT + FMSA is shown to give better performance than FMSA for mid- and long-range attractions. For short-range and very short-range attractions, the theory successfully corrects the deficiencies of the original FMSA. Comparisons include the evaluation of contact values, gap height at a discontinuity and profiles of the RDF. This work provides an accurate and consistent way to handle the SW potential.     

Corrections to the density-functional theory electronic spectrum: copper phthalocyanine

A method for improving the electronic spectrum of standard Density-Functional Theory (DFT) calculations (i.e., LDA or GGA approximations) is presented, and its application is discussed for the case of the copper phthalocyanine (CuPc) molecule. The method is based on a treatment of exchange and correlation in a many-body Hamiltonian, and it leads to easy-to-evaluate corrections to the DFT eigenvalues. Self-interaction is largely corrected, so that the modified energy levels do not suffer from spurious crossings, as often encountered for CuPc in DFT, and they remedy the standard underestimation of the gap. As a specific example we study the sequence and position of the CuPc molecular orbitals, which are wrongly calculated by standard DFT, and show that they are correctly reproduced after our corrections are included. The suggested method is fast and simple and, while not as accurate as hybrid or semiempirical functionals for molecular levels, it can be easily applied to any local-orbital DFT approach, improving on several important limitations of standard DFT methods.