O. V. Gritsenko

Molecular calculations of excitation energies and (hyper)polarizabilities.

An approximate Kohn–Sham exchange-correlation potential νxcSAOP is developed with the method of statistical averaging of (model) orbital potentials (SAOP) and is applied to the calculation of excitation energies as well as of static and frequency-dependent multipole polarizabilities and hyperpolarizabilities within time-dependent density functional theory (TDDFT). νxcSAOP provides high quality results for all calculated response properties and a substantial improvement upon the local density approximation (LDA) and the van Leeuwen–Baerends (LB) potentials for the prototype molecules CO, N2, CH2O, and C2H4. For the first three molecules and the lower excitations of the C2H4 the average error of the vertical excitation energies calculated with νxcSAOP approaches the benchmark accuracy of 0.1 eV for the electronic spectra.

Shape corrections to exchange-correlation potentials by gradient-regulated seamless connection of model potentials for inner and outer region

Shape corrections to the standard approximate Kohn-Sham exchange-correlation (xc) potentials are considered with the aim to improve the excitation energies (especially for higher excitations) calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection (GRAC) of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends (LB) are seamlessly connected to the (shifted) xc potential of Becke and Perdew (BP) with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N2, CO, CH2O, C2H4, C5NH5, C6H6, Li2, Na2, K2. The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of (model) orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, whic...

Asymptotic correction of the exchange-correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations

Time-dependent density functional theory (TDDFT) calculations of charge-transfer excitation energies omegaCT are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange-correlation kernel fxc. We relate the error to the physical meaning of the orbital energy of the Kohn-Sham lowest unoccupied molecular orbital (LUMO). The LUMO orbital energy in Kohn-Sham DFT--in contrast to the Hartree-Fock model--approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of fxc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel fxc(asymp) is proposed. The importance of the asymptotic correction of fxc is demonstrated with the calculation of omegaCT(R) for the prototype diatomic system HeBe at various separations R(He-Be). The TDDFT-ALDA curve omegaCT(R) roughly resembles the benchmark ab initio curve omegaCT CISD(R) of a configuration interaction calculation with single and double excitations in the region R=1-1.5 A, where a sizable He-Be interaction exists, but exhibits the wrong behavior omegaCT(R)<<omegaCT CISD(R) at large R. The TDDFT curve obtained with fxc (asymp) however approaches omegaCT CISD(R) closely in the region R=3-10 A. Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and fxc(asymp) for weakly interacting fragments and suitable interpolation expressions are considered.

Improved density functional theory results for frequency‐dependent polarizabilities, by the use of an exchange‐correlation potential with correct asymptotic behavior

The exchange-correlation potentials v xc which are currently fashionable in density functional theory ~DFT!, such as those obtained from the local density approximation ~LDA! or generalized gradient approximations ~GGAs!, all suffer from incorrect asymptotic behavior. In atomic calculations, this leads to substantial overestimations of both the static polarizability and the frequency dependence of this property. In the present paper, it is shown that the errors in atomic static dipole and quadrupole polarizabilities are reduced by almost an order of magnitude, if a recently proposed model potential with correct Coulombic long-range behavior is used. The frequency dependence is improved similarly. The model potential also removes the overestimation in molecular polarizabilities, leading to slight improvements for average molecular polarizabilities and their frequency dependence. For the polarizability anisotropy we find that the model potential results do not improve over the LDA and GGA results. Our method for calculating frequency-dependent molecular response properties within time-dependent DFT, which we described in more detail elsewhere, is summarized.

Exchange and correlation energy in density functional theory. Comparison of accurate DFT quantities with traditional Hartree-Fock based ones and generalized gradient approximations for the molecules Li2, N2, F2.

The density functional definition of exchange and correlation differs from the traditional one. In order to calculate the density functional theory (DFT), quantities accurately, molecular Kohn–Sham (KS) solutions have been obtained from ab initio wave functions for the homonuclear diatomic molecules Li2, N2, F2. These afford the construction of the KS determinant Ψs and the calculation of its total electronic energy EKS and the kinetic, nuclear-attraction and Coulomb repulsion components Ts, V, WH as well as the (DFT) exchange energy Ex and correlation energy Ec. Comparison of these DFT quantities has been made on one hand with the corresponding Hartree–Fock (HF) quantities and on the other hand with local density approximation (LDA) and generalized gradient approximation (GGA). Comparison with HF shows that the correlation errors in the components T, V, and WH of the total energy are much larger for HF than KS determinantal wave functions. However, the total energies EKS and EHF appear to be close to eac...

An improved density matrix functional by physically motivated repulsive corrections

An improved density matrix functional [correction to Buijse and Baerends functional (BBC)] is proposed, in which a hierarchy of physically motivated repulsive corrections is employed to the strongly overbinding functional of Buijse and Baerends (BB). The first correction C1 restores the repulsive exchange-correlation (xc) interaction between electrons in weakly occupied natural orbitals (NOs) as it appears in the exact electron pair density rho(2) for the limiting two-electron case. The second correction C2 reduces the xc interaction of the BB functional between electrons in strongly occupied NOs to an exchange-type interaction. The third correction C3 employs a similar reduction for the interaction of the antibonding orbital of a dissociating molecular bond. In addition, C3 applies a selective cancellation of diagonal terms in the Coulomb and xc energies (not for the frontier orbitals). With these corrections, BBC still retains a correct description of strong nondynamical correlation for the dissociating electron pair bond. BBC greatly improves the quality of the BB potential energy curves for the prototype few-electron molecules and in several cases BBC reproduces very well the benchmark ab initio potential curves. The average error of the self-consistent correlation energies obtained with BBC3 for prototype atomic systems and molecular systems at the equilibrium geometry is only ca. 6%.

On the required shape corrections to the local density and generalized gradient approximations to the Kohn–Sham potentials for molecular response calculations of (hyper)polarizabilities and excitation energies

It is well known that shape corrections have to be applied to the local-density (LDA) and generalized gradient (GGA) approximations to the Kohn–Sham exchange–correlation potential in order to obtain reliable response properties in time dependent density functional theory calculations. Here we demonstrate that it is an oversimplified view that these shape corrections concern primarily the asymptotic part of the potential, and that they affect only Rydberg type transitions. The performance is assessed of two shape-corrected Kohn–Sham potentials, the gradient-regulated asymptotic connection procedure applied to the Becke–Perdew potential (BP–GRAC) and the statistical averaging of (model) orbital potentials (SAOP), versus LDA and GGA potentials, in molecular response calculations of the static average polarizability α, the Cauchy coefficient S−4, and the static average hyperpolarizability β. The nature of the distortions of the LDA/GGA potentials is highlighted and it is shown that they introduce many spuriou...

Physical interpretation and evaluation of the Kohn-Sham and Dyson components of the epsilon-I relations between the Kohn-Sham orbital energies and the ionization potentials

Theoretical and numerical insight is gained into the e–I relations between the Kohn–Sham orbital energies ei and relaxed vertical ionization potentials (VIPs) Ij, which provide an analog of Koopmans’ theorem for density functional theory. The Kohn–Sham orbital energy ei has as leading term −niIi−∑j∈Ωs(i)njIj, where Ii is the primary VIP for ionization (φi)−1 with spectroscopic factor (proportional to the intensity in the photoelectron spectrum) ni close to 1, and the set Ωs(i) contains the VIPs Ij that are satellites to the (φi)−1 ionization, with small but non-negligible nj. In addition to this “average spectroscopic structure” of the ei there is an electron-shell step structure in ei from the contribution of the response potential vresp. Accurate KS calculations for prototype second- and third-row closed-shell molecules yield valence orbital energies −ei, which correspond closely to the experimental VIPs, with an average deviation of 0.08 eV. The theoretical relations are numerically investigated in cal...

Excitation energies of dissociating H2: a problematic case for the adiabatic approximation of time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is applied for calculation of the excitation energies of the dissociating H2 molecule. The standard TDDFT method of adiabatic local density approximation (ALDA) totally fails to reproduce the potential curve for the lowest excited singlet 1Σu+ state of H2. Analysis of the eigenvalue problem for the excitation energies as well as direct derivation of the exchange-correlation (xc) kernel fxc(r,r′,ω) shows that ALDA fails due to breakdown of its simple spatially local approximation for the kernel. The analysis indicates a complex structure of the function fxc(r,r′,ω), which is revealed in a different behavior of the various matrix elements K1c,1cxc (between the highest occupied Kohn–Sham molecular orbital ψ1 and virtual MOs ψc) as a function of the bond distance R(H–H). The effect of nonlocality of fxc(r,r′) is modeled by using different expressions for the corresponding matrix elements of different orbitals. Asymptotically corrected ALDA (ALDA-AC) expressions...

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn–Sham (KS) exchange potential vxσCEDA is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green’s function, which preserves the essential structure of the density response function. vxσCEDA is an explicit functional of the occupied KS orbitals, which has the Slater vSσ and response vrespσCEDA potentials as its components. The latter exhibits the characteristic step structure with “diagonal” contributions from the orbital densities |ψiσ|2, as well as “off-diagonal” ones from the occupied–occupied orbital products ψiσψj(≠1)σ*. Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger–Li–Iafrate (KLI), exact exchange (EXX), and Hartree–Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical “closure approximations” to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies ...