Density functional for spectroscopy: no long-range self-interaction error, good performance for Rydberg and charge-transfer states, and better performance on average than B3LYP for ground states

We present a new density functional called M06-HF. The new functional has full Hartree-Fock exchange, and therefore it eliminates self-exchange interactions at long range. This leads to good performance in TDDFT calculations of both Rydberg and charge-transfer states. In addition, the functional satisfies the uniform electron gas limit, and it is better than the popular B3LYP functional, on average, for ground-electronic-state energetics.     

Doubly excited Rydberg states of He I and Ba I

The Auger decay widths of doubly-excited Rydberg states of He I and Ba I have been calculated by the multi-configuration Hartree-Fock procedure. The configuration mixing is crucial in obtaining the correct widths, while the energies seem to be relatively less sensitive to mixing. The usual mixing procedure is often unstable for doubly excited states and careful selection of configurations is required. An improved procedure for selecting the states for mixing is formulated, which seems to stabilize the calculation of both the energies and widths, with small numbers of configurations which are mixed. We apply the recipe to a selected set of doubly excited states of He and Ba. The long standing discrepancies in the widths for the series 7sns, 7snd, 8sns, and 8snd of Ba I withn > 11 may be explained by this procedure, except for the 7snd series. The calculated widths for the 7snd series are larger than the experimental values by a factor of 10–20. The difficulties of treating the states with both electrons in higher Rydberg orbitals are discussed.     

Rydberg states with quantum Monte Carlo

Calculations on Rydberg states are performed using quantum Monte Carlo methods. Excitation energies and singlet-triplet splittings are calculated for two model systems, the carbon atom (3P and 1P) and carbon monoxide ((1Sigma and 3Sigma). Kohn-Sham wave functions constructed from open-shell localized Hartree-Fock orbitals are used as trial and guide functions. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method depends strongly on the wave function's nodal hypersurface. Nodal artefacts are investigated for the ground state of the carbon atom. Their effect on the FN-DMC results can be analyzed quantitatively. FN-DMC leads to accurate excitation energies but to less accurate singlet-triplet splittings. Variational Monte Carlo calculations are able to reproduce the experimental results for both the excitation energies and the singlet-triplet splittings.     

Basis-set quality and basis-set bias in molecular property calculations

Quality measures for Gaussian basis sets are proposed that are based on principal angles between the basis set and reference molecular orbitals. The principal angles are obtained from the cosine-sine (CS) decomposition of orthogonal matrices and yield detailed information about basis-set convergence with respect to different regions of space. Principal angles for occupied orbitals show excellent correlation with basis-set errors in ground-state energies. Furthermore, ground-state bias in finite basis sets can be estimated from the relation between principal angles for occupied and Rydberg orbitals. Ground-state bias is observed in basis sets including extensive diffuse augmentation and affects the quality of computed molecular response properties. Principal angles and ground-state bias are investigated for the H-Ne atoms and a series of diatomics using numerical Hartree-Fock calculations as a reference. Convergence of ground-state energies and static polarizabilities is studied for the hierarchies of correlation-consistent and Karlsruhe segmented def2 basis sets including different levels of diffuse augmentation.     

Open-shell localized Hartree-Fock method based on the generalized adiabatic connection Kohn-Sham formalism for a self-consistent treatment of excited states

An effective exact-exchange Kohn-Sham approach for the treatment of excited electronic states, the generalized adiabatic connection open-shell localized Hartree-Fock (GAC-OSLHF) method is presented. The GAC-OSLHF method is based on the generalized adiabatic connection Kohn-Sham formalism and therefore capable of treating excited electronic states, which are not the energetically lowest of their symmetry. The method is self-interaction free and allows for a fully self-consistent computation of excited valence as well as Rydberg states. Results for atoms and small- and medium-size molecules are presented and compared to restricted open-shell Hartree-Fock (ROHF) and time-dependent density-functional results as well as to experimental data. While GAC-OSLHF and ROHF results are quite close to each other, the GAC-OSLHF method shows a much better convergence behavior. Moreover, the GAC-OSLHF method as a Kohn-Sham method, in contrast to the ROHF approach, represents a framework which allows also for a treatment of correlation besides an exchange by appropriate functionals. In contrast to the common time-dependent density-functional methods, the GAC-OSLHF approach is capable of treating doubly or multiply excited states and can be easily applied to molecules with an open-shell ground state. On the nodal planes of the energetically highest occupied orbital, the local multiplicative GAC-OSLHF exchange potential asymptotically approaches a different, i.e., nonzero, value than in other regions, an asymptotic behavior which is known from exact Kohn-Sham exchange potentials of ground states of molecules.     

Dynamic polarizabilities and Rydberg states of open shell atomic systems

Time dependent coupled Hartree-Fock (TDCHF) theory is applied to calculate frequency dependent polarizabilities, transition energies, oscillator strengths and effective quantum numbers of several excited states of the open shell ions Al, Si⁺, P²⁺, S³⁺, Cl⁴⁺, Ar⁵⁺, Cl and Ar⁺ in the ²P state within and beyond the normal dispersion region. The Roothaan formalism has been adopted to deal with the open shell problem. The excitation energies are extracted from the positions of the poles of an appropriate functional. Analytic representations of the singly excited Rydberg states have been found. The results obtained compare well with spectroscopic and other elaborate theoretical data wherever available. Inner shell excitations have been found for the first time within TDCHF theory.     

Two new double Rydberg anions plus access to excited states of neutral Rydberg radicals via anion photoelectron spectroscopy

We have observed and characterized two new double Rydberg anions N6H19- and N7H22- through their anion photoelectron spectra. The vertical detachment energies of these anions were found to be 0.443 and 0.438 eV, respectively. In addition, for three of the seven double Rydberg anions now known, we measured photodetachment transitions not only to the ground electronic states of their corresponding neutral Rydberg radicals but also to their first electronically excited states. In each spectrum, the energy spacing between the resulting peaks provided the ground-to-first electronically excited-state transition energy for the double Rydberg anion's corresponding neutral Rydberg radical. For the radicals, N4H13, N5H16, and N6H19, the spacings were found to be 0.83, 0.70, and 0.67 eV, respectively. These values are in excellent agreement with ground-to-first excited-state transition energies measured in absorption for the same neutral Rydberg radicals by Fuke and co-workers [Eur. Phys. J. D 9, 309 (1999); J. Phys. Chem. A 106, 5242 (2002).] The duplication of this neutral Rydberg property by photodetachment of double Rydberg anions further confirms that double Rydberg anions are indeed the negative ions of their corresponding neutral Rydberg molecules and cluster-like systems.     

Dyson orbitals for ionization from the ground and electronically excited states within equation-of-motion coupled-cluster formalism: theory, implementation, and examples

Implementation of Dyson orbitals for coupled-cluster and equation-of-motion coupled-cluster wave functions with single and double substitutions is described and demonstrated by examples. Both ionizations from the ground and electronically excited states are considered. Dyson orbitals are necessary for calculating electronic factors of angular distributions of photoelectrons, Compton profiles, electron momentum spectra, etc, and can be interpreted as states of the leaving electron. Formally, Dyson orbitals represent the overlap between an initial N-electron wave function and the N-1 electron wave function of the corresponding ionized system. For the ground state ionization, Dyson orbitals are often similar to the corresponding Hartree-Fock molecular orbitals (MOs); however, for ionization from electronically excited states Dyson orbitals include contributions from several MOs and their shapes are more complex. The theory is applied to calculating the Dyson orbitals for ionization of formaldehyde from the ground and electronically excited states. Partial-wave analysis is employed to compute the probabilities to find the ejected electron in different angular momentum states using the freestanding and Coulomb wave representations of the ionized electron. Rydberg states are shown to yield higher angular momentum electrons, as compared to valence states of the same symmetry. Likewise, faster photoelectrons are most likely to have higher angular momentum.     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

Comments about the representation of Rydberg and ionic excited states and their photochemistry

This paper discusses the conditions for representing Rydberg and ionic excited states of molecules. It especially shows the intrinsic difficulties of MO methods to treat the weak resonances between strongly polarized situations in highly polarizable symmetric systems; such situations occur in the long distance region for Rydberg excited states of homonuclear molecules, and for the 90 ° twisted singlet excited states of polyenes. The valence/Rydberg mixing is discussed, and some principles for the understanding of Rydberg photochemistry are proprosed, based on a few examples. The present knowledge of the photochemistry of zwitterionic excited states of polyenes is summarized.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.     

The role of excited Rydberg States in electron transfer dissociation

Ab initio electronic structure methods are used to estimate the cross sections for electron transfer from donor anions having electron binding energies ranging from 0.001 to 0.6 eV to each of three sites in a model disulfide-linked molecular cation. The three sites are (1) the S-S sigma(*) orbital to which electron attachment is rendered exothermic by Coulomb stabilization from the nearby positive site, (2) the ground Rydberg orbital of the -NH(3)(+) site, and (3) excited Rydberg orbitals of the same -NH(3)(+) site. It is found that attachment to the ground Rydberg orbital has a somewhat higher cross section than attachment to either the sigma orbital or the excited Rydberg orbital. However, it is through attachment either to the sigma(*) orbital or to certain excited Rydberg orbitals that cleavage of the S-S bond is most likely to occur. Attachment to the sigma(*) orbital causes prompt cleavage because the sigma energy surface is repulsive (except at very long range). Attachment to the ground or excited Rydberg state causes the S-S bond to rupture only once a through-bond electron transfer from the Rydberg orbital to the S-S sigma(*) orbital takes place. For the ground Rydberg state, this transfer requires surmounting an approximately 0.4 eV barrier that renders the S-S bond cleavage rate slow. However, for the excited Rydberg state, the intramolecular electron transfer has a much smaller barrier and is prompt.     

Benchmarking the performance of time-dependent density functional methods

The performance of 24 density functionals, including 14 meta-generalized gradient approximation (mGGA) functionals, is assessed for the calculation of vertical excitation energies against an experimental benchmark set comprising 14 small- to medium-sized compounds with 101 total excited states. The experimental benchmark set consists of singlet, triplet, valence, and Rydberg excited states. The global-hybrid (GH) version of the Perdew-Burke-Ernzerhoff GGA density functional (PBE0) is found to offer the best overall performance with a mean absolute error (MAE) of 0.28 eV. The GH-mGGA Minnesota 2006 density functional with 54% Hartree-Fock exchange (M06-2X) gives a lower MAE of 0.26 eV, but this functional encounters some convergence problems in the ground state. The local density approximation functional consisting of the Slater exchange and Volk-Wilk-Nusair correlation functional (SVWN) outperformed all non-GH GGAs tested. The best pure density functional performance is obtained with the local version of the Minnesota 2006 mGGA density functional (M06-L) with an MAE of 0.41 eV.     

Jahn-Teller effect in Rydberg series: a multi-state vibronic coupling problem

Two simple limiting cases of Jahn-Teller (JT) coupling in Rydberg states of polyatomic molecules are considered, namely(i) JT coupling in Rydberg orbitals as well as in the ionization continuum (nondegenerate ion core, degenerate Rydberg series) and(ii) JT coupling in the ion core (degenerate ion core, nondegenerate Rydberg series). For both models simple and efficient algorithms for the computation of spectra (dynamical JT effect) are developed. The orbital JT effect is shown to represent a novel type of multi-state vibronic coupling, giving rise to interesting spectroscopic phenomena, among them resonant inter-Rydberg perturbations and JT induced autoionization. Particular attention is paid to the demonstration of the characteristic spectroscopic signatures of the two types of JT coupling in Rydberg states.     

Study of Wave Functions and Radiation Transitions in a Rydberg Polar Cluster Using the Continuum Model

A continuum model describing highly excited (Rydberg) electronic states in clusters composed of polar molecules was proposed. On the basis of this model, the wave functions of Rydberg electronic states of clusters were calculated for a wide range of characteristic cluster parameters. These states are not hydrogen-like and can be described using the quantum defect theory. This fact indicates that radiative transitions can be forbidden within certain ranges of cluster parameters. The quantum defects in clusters and the lifetimes of different states were calculated. The possibility of formation of metastable Rydberg states and anomalous spectral characteristics of Rydberg clusters was shown.