Dennis R. Salahub

Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold

This paper presents an evaluation of the performance of time-dependent density-functional response theory (TD-DFRT) for the calculation of high-lying bound electronic excitation energies of molecules. TD-DFRT excitation energies are reported for a large number of states for each of four molecules: N2, CO, CH2O, and C2H4. In contrast to the good results obtained for low-lying states within the time-dependent local density approximation (TDLDA), there is a marked deterioration of the results for high-lying bound states. This is manifested as a collapse of the states above the TDLDA ionization threshold, which is at ??HOMOLDA (the negative of the highest occupied molecular orbital energy in the LDA). The ??HOMOLDA is much lower than the true ionization potential because the LDA exchange-correlation potential has the wrong asymptotic behavior. For this reason, the excitation energies were also calculated using the asymptotically correct potential of van Leeuwen and Baerends (LB94) in the self-consistent field step. This was found to correct the collapse of the high-lying states that was observed with the LDA. Nevertheless, further improvement of the functional is desirable. For low-lying states the asymptotic behavior of the exchange-correlation potential is not critical and the LDA potential does remarkably well. We propose criteria delineating for which states the TDLDA can be expected to be used without serious impact from the incorrect asymptotic behavior of the LDA potential

Dynamic polarizabilities and excitation spectra from a molecular implementation of time‐dependent density‐functional response theory: N2 as a case study

We report the implementation of time‐dependent density‐functional response theory (TD‐DFRT) for molecules using the time‐dependent local density approximation (TDLDA). This adds exchange and correlation response terms to our previous work which used the density‐functional theory (DFT) random phase approximation (RPA) [M. E. Casida, C. Jamorski, F. Bohr, J. Guan, and D. R. Salahub, in Theoretical and Computational Modeling of NLO and Electronic Materials, edited by S. P. Karna and A. T. Yeates (ACS, Washington, D.C., in press)], and provides the first practical, molecular DFT code capable of treating frequency‐dependent response properties and electronic excitation spectra based on a formally rigorous approach. The essentials of the method are described, and results for the dynamic mean dipole polarizability and the first eight excitation energies of N2 are found to be in good agreement with experiment and with results from other ab initio methods.

Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with ab initio quantum mechanics calculations

Standard density functional theory (DFT) is augmented with a damped empirical dispersion term. The damping function is optimized on a small, well balanced set of 22 van der Waals (vdW) complexes and verified on a validation set of 58 vdW complexes. Both sets contain biologically relevant molecules such as nucleic acid bases. Results are in remarkable agreement with reference high‐level wave function data based on the CCSD(T) method. The geometries obtained by full gradient optimization are in very good agreement with the best available theoretical reference. In terms of the standard deviation and average errors, results including the empirical dispersion term are clearly superior to all pure density functionals investigated—B‐LYP, B3‐LYP, PBE, TPSS, TPSSh, and BH‐LYP—and even surpass the MP2/cc‐pVTZ method. The combination of empirical dispersion with the TPSS functional performs remarkably well. The most critical part of the empirical dispersion approach is the damping function. The damping parameters should be optimized for each density functional/basis set combination separately. To keep the method simple, we optimized mainly a single factor, sR, scaling globally the vdW radii. For good results, a basis set of at least triple‐ζ quality is required and diffuse functions are recommended, since the basis set superposition error seriously deteriorates the results. On average, the dispersion contribution to the interaction energy missing in the DFT functionals examined here is about 15 and 100% for the hydrogen‐bonded and stacked complexes considered, respectively.

Semiempirical Quantum Chemical PM6 Method Augmented by Dispersion and H-Bonding Correction Terms Reliably Describes Various Types of Noncovalent Complexes.

Because of its construction and parametrization for more than 80 elements, the semiempirical quantum chemical PM6 method is superior to other similar methods. Despite its advantages, however, the PM6 method fails for the description of noncovalent interactions, specifically the dispersion energy and H-bonding. Upon inclusion of correction terms for dispersion and H-bonding, the performance of the method was found to be dramatically improved. The former correction included two parameters in the damping function that were parametrized to reproduce the benchmark interaction energies [CCSD(T)/complete basis set (CBS) limit] of the dispersion-bonded complexes from the S22 data set. The latter correction was parametrized on an extended set of H-bonded stabilization energies determined at the MP2/cc-pVTZ level. The resulting PM6-DH method was tested on the S22 data set, for which chemical accuracy (error < 1 kcal/mol) was achieved, and also on the JSCH2005 set, for which significant improvement over the original PM6 method was also obtained. Implementation of analytical gradients allows very efficient geometry optimization, which, for all complexes, provides better agreement with the benchmark data. Excellent results were also achieved for small peptides, and here again, chemical accuracy was obtained (i.e., the error with respect to CCSD(T)/CBS results was smaller than 1 kcal/mol). The performance of the technique was finally demonstrated on extended complexes, namely, the porphine dimer and various graphene models with DNA bases and base pairs, where the PM6-DH stabilization energies agree very well with available benchmark data obtained with DFT-D, SCS-MP2, and MP2.5 methods. The PM6-DH calculations are very efficient and can be routinely applied for systems of up to 1000 atoms. For nonaromatic systems, the use of a linear scaling version of the SCF procedure based on localized orbitals speeds up the method significantly and allows one to investigate systems with several thousand atoms. The method can thus replace force fields, which face basic problems for the description of quantum effects, in many applications.

Asymptotic correction approach to improving approximate exchange–correlation potentials: Time-dependent density-functional theory calculations of molecular excitation spectra

The time-dependent density functional theory (TD-DFT) calculation of excitation spectra places certain demands on the DFT exchange–correlation potential, vxc, that are not met by the functionals normally used in molecular calculations. In particular, for high-lying excitations, it is crucial that the asymptotic behavior of vxc be correct. In a previous paper, we introduced a novel asymptotic-correction approach which we used with the local density approximation (LDA) to yield an asymptotically corrected LDA (AC-LDA) potential [Casida, Casida, and Salahub, Int. J. Quantum Chem. 70, 933 (1998)]. The present paper details the theory underlying this asymptotic correction approach, which involves a constant shift to incorporate the effect of the derivative discontinuity (DD) in the bulk region of finite systems, and a spliced asymptotic correction in the large r region. This is done without introducing any adjustable parameters. We emphasize that correcting the asymptotic behavior of vxc is not by itself suffi...

Charge-transfer correction for improved time-dependent local density approximation excited-state potential energy curves: Analysis within the two-level model with illustration for H2 and LiH

Time-dependent density-functional theory (TDDFT) is an increasingly popular approach for calculating molecular excitation energies. However, the TDDFT lowest triplet excitation energy, ωT, of a closed-shell molecule often falls rapidly to zero and then becomes imaginary at large internuclear distances. We show that this unphysical behavior occurs because ωT2 must become negative wherever symmetry breaking lowers the energy of the ground state solution below that of the symmetry unbroken solution. We use the fact that the ΔSCF method gives a qualitatively correct first triplet excited state to derive a “charge-transfer correction” (CTC) for the time-dependent local density approximation (TDLDA) within the two-level model and the Tamm-Dancoff approximation (TDA). Although this correction would not be needed for the exact exchange–correlation functional, it is evidently important for a correct description of molecular excited state potential energy surfaces in the TDLDA. As a byproduct of our analysis, we sh...

Model potential calculations for second‐row transition metal molecules within the local‐spin‐density method

The model potential (MP) method originally proposed by Huzinaga and Bonifacic is extended to spin‐polarized local‐spin‐density calculations, including scalar relativistic effects. The theoretical justification of the MP method in this case is studied and the method of optimization of the basis functions and MP parameters is given. The validity of the frozen core approximation is studied for Mo2, Ru2, and Ag2. It is found that the MP can very accurately reproduce all‐electron (AE) results if the 4p electrons of Ag and the 3d electrons of Mo are also considered as valence electrons, although inclusion of these electrons in the core still yields a useful level of accuracy. It is shown that the present MP results are not sensitive to basis set superposition errors (BSSE). Upon inclusion of the scalar relativistic effects the calculated bond length and vibrational frequency of Ag2 are in near perfect agreement with experiment, while the dissociation energy is overestimated by 23% with the ‘‘best’’ local potent...

The structure of Nb3O and Nb3O+ determined by pulsed field ionization–zero electron kinetic energy photoelectron spectroscopy and density functional theory

The geometrical structures of the ground states of triniobium monoxide, Nb3O, and its cation, Nb3O+, have been determined by an experimental and theoretical study. Vibrationally resolved photoelectron spectra of an Nb3O cluster beam were obtained at 100 and 300 K using the pulsed field ionization‐zero electron kinetic energy technique. The spectra were simulated by calculating multidimensional Franck–Condon factors using the geometries and harmonic vibrational frequencies obtained from density functional theory for the minimum energy structures of the ion and neutral molecule. The rather remarkable agreement between the experiment and the simulated spectra establishes that Nb3O and Nb3O+ have planar C2v structures with the oxygen atom bridging two niobium atoms. These are the most complex transition metal cluster structures to date to be characterized by gas phase spectroscopic techniques.

Ground and excited states of group IVA diatomics from local‐spin‐density calculations: Model potentials for Si, Ge, and Sn

LCGTO‐MP‐LSD results are reported for the spectroscopic constants and electronic structure of the diatomic molecules Si2, Ge2, Sn2, SiGe, SiSn, and GeSn in their low‐lying electronic states. For the homonuclear molecules we found that the ground state is 3Σ−g with the most important lower‐lying excited states being 3Πu, 1Πu, and 1Σ+g, respectively. Our results are in good agreement with the available experimental data and also in qualitative agreement with other theoretical studies. We present here the first theoretical study on the heteronuclear molecules, for which experimental data are not available. We found the 3Σ− state to be the lowest, followed by 3Π and 1Σ+ states. Model potentials (MP) are reported for the Si, Ge, and Sn atoms. The reliable results for molecules complement those for the atoms and show that the LSD model potentials presented here allow for an accurate description of chemical bonding and spectroscopic properties in the title molecules.

Nuclear magnetic resonance spin-spin coupling constants from density functional theory: Problems and results

Our recently developed method for the calculation of indirect nuclear spin–spin coupling constants is studied in more detail. For the couplings between nuclei other than N, O, and F (which have lone pairs) the method yields very reliable results. The results for 1J(Si–H) couplings are presented and their dependence on the basis set quality is analyzed. Also, 2J(H–H) and 1J(X–H) couplings (X=C, Si, Ge, Sn) in XH4 molecules are presented and the relativistic effects on 1J(X–H) are discussed. The limitations of the method, which is based on density functional theory, are connected with the inability of the present LDA and GGA exchange‐correlation functionals to describe properly the spin‐perturbations (through the Fermi‐contact mechanism) on atoms to the right of the periodic table (containing lone pairs). However, the deviations from experiment of the calculated couplings for such nuclei are systematic, at least for one‐bond couplings, and therefore these calculated couplings should still be useful for NMR ...