A family of intracules, a conjecture and the electron correlation problem

We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.     

A CASSCF/CASPT2 study on the low-lying excited states of HSiCN, HSiNC and their ions

Equilibrium geometries of low-lying electronic states of cyanosilylene (HSiCN), isocyanosilylene (HSiNC), and their ions have been investigated using the complete active space self-consistent field (CASSCF) approach. The harmonic vibrational frequencies on the optimized geometries were calculated using the multiconfiguration linear response (MCLR) method. Taking the further correlation effects into account, the complete active space perturbation theory of second-order (CASPT2) was carried out for the energetic correction. The CASPT2 calculations have been performed to obtain the vertical excitation energies of selected low-lying excited states of HSiCN and HSiNC. Computed results show that the singlet-triplet splittings are calculated to be 0.99 and 1.30 eV for HSiCN and HSiNC, respectively. The vertical excitation energies of the lowest singlet and triplet excited states in HSiCN are lower than those in HSiNC. The first vertical ionization energy of HSiCN (10.04 eV) is higher than that of HSiNC (9.97 eV). The ground-state adiabatic electron affinities are found to be rather high, and the value of HSiCN (1.85 eV) higher than that of HSiNC (1.52 eV). The existences of dipole-bound excited negative ion states have been discovered within HSiCN and HSiNC.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Ab initio CI calculations on benzene with an extended basis set

An extended basis set of triple zeta plus polarization quality is employed to carry out configuration interaction (CI ) calculations of the three lowest singlet and triplet excited states of benzene. The CI calculation is carried out by taking into account single and double excitations of π and σ electrons. In the CI , composite natural orbitals (CNO s), which are constructed from the natural orbitals of the ground state of ethylene, are used as virtual orbitals. The aim of using CNOs is to reduce the number of virtual orbitals to be used in constructing configuration-state functions, thus cutting down CI dimensions without losing reasonable accuracy. The excitation energies resulting from the CI are in fairly good agreement with experiment. The root mean square of the deviation is 0.22 eV for the six calculated energies and the largest disagreement is 0.37 eV for the third singlet excited state. To obtain better excitation energies by an ab initio calculation, it seems likely that we need to take into account more electron correlation than in the present calculation. © 1994 John Wiley & Sons, Inc.     

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.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Chemical effects of low energy electron impact on hydrocarbons in the gas phase: III. Cyclopropane

The simulated radiolysis of cyclopropane with low energy electrons (3.5 to 15.0 eV) was investigated. The setup used for the irradiations has been described previously. Appearance curves of the various products formed under electron impact were determined. The features observed on these curves yield various indications.(1) Some products arise from the dissociation of excited molecules. Contributing states are the following ones: a triplet state at 7.4 eV, singlet states at 6.7 and/or 7.7 eV, at 8.55 eV, at 9.4 and/or 9.95 eV and superexcited states lying around 10.2 eV. As in other hydrocarbons studied, the electron impact excitation cross section shows a steep increase at the ionization potential. (2) Other products result from ion fragmentation and ion—molecule reactions.A reaction scheme was proposed to account for the chemical effects associated with excited states and the yields of excited molecules in dissociating states were derived from experimental data. The observations relative to excited molecule fragmentation are in conformity with photolysis data. Additional information on the decomposition processes of molecules excited in the triplet state at 7.4 eV, in the singlet states at 6.7 and/or 7.7 eV and in the superexcited states were obtained.Owing to the complexity of ionic mechanisms it was not possible to distinguish between the contributions of ionization and excitation. Only the radiation chemical yield of products, G(products), was evaluated. The values found for G(products) just above the ionization potential are close to the data obtained in conventional radiolysis which could indicate that secondary electrons having such energies play an important role in radiation chemistry.     

Effect of microhydration on the electronic structure of the chromophores of the photoactive yellow and green fluorescent proteins

Electronic structure calculations of microhydrated model chromophores (in their deprotonated anionic forms) of the photoactive yellow and green fluorescent proteins (PYP and GFP) are reported. Electron-detachment and excitation energies as well as binding energies of mono- and dihydrated isomers are computed and analyzed. Microhydration has different effects on the excited and ionized states. In lower-energy planar isomers, the interaction with one water molecule blueshifts the excitation energies by 0.1-0.2 eV, whereas the detachment energies increase by 0.4-0.8 eV. The important consequence is that microhydration by just one water molecule converts the resonance (autoionizing) excited states of the bare chromophores into bound states. In the lower-energy microhydrated clusters, interactions with water have negligible effect on the chromophore geometry; however, we also identified higher-energy dihydrated clusters of PYP in which two water molecules form hydrogen-bonding network connecting the carboxylate and phenolate moieties and the chromophore is strongly distorted resulting in a significant shift of excitation energies (up to 0.6 eV).     

Quantum chemical modeling of photoadsorption properties of the nitrogen-vacancy point defect in diamond

Quantum chemical calculations of geometric and electronic structure and vertical transition energies for several low-lying excited states of the neutral and negatively charged nitrogen-vacancy point defect in diamond (NV(0) and NV(-)) have been performed employing various theoretical methods and basis sets and using finite model NC(n)H(m) clusters. Unpaired electrons in the ground doublet state of NV(0) and triplet state of NV(-) are found to be localized mainly on three carbon atoms around the vacancy and the electronic density on the nitrogen and rest of C atoms is only weakly disturbed. The lowest excited states involve different electronic distributions on molecular orbitals localized close to the vacancy and their wave functions exhibit a strong multireference character with significant contributions from diffuse functions. CASSCF calculations underestimate excitation energies for the anionic defect and overestimate those for the neutral system. The inclusion of dynamic electronic correlation at the CASPT2 level leads to a reasonable agreement (within 0.25 eV) of the calculated transition energy to the lowest excited state with experiment for both systems. Several excited states for NV(-) are found in the energy range of 2-3 eV, but only for the 1(3)E and 5(3)E states the excitation probabilities from the ground state are significant, with the first absorption band calculated at approximately 1.9 eV and the second lying 0.8-1 eV higher in energy than the first one. For NV(0), we predict the following order of electronic states: 1(2)E (0.0), 1(2)A(2) (approximately 2.4 eV), 2(2)E (2.7-2.8 eV), 1(2)A(1), 3(2)E (approximately 3.2 eV and higher).     

A TDDFT study of the low-lying excitation energies of polycyclic cinnolines and their carbocyclic analogues

The low-lying excited states of 21 compounds of polycyclic cinnoline, monoaza-hydrocarbon and their corresponding polycyclic aromatic hydrocarbon (PAH) analogues have been investigated in the framework of time-dependent density functional theory (TDDFT). The gradient corrected BLYP, hybrid B3LYP and B3P86 functionals together with 6-31G (d) basis set have been used. The hybrid-type B3LYP and B3P86 systematically overestimate the excitation energies for states with dominating ionic character (corresponding to group III band), with a mean absolute deviation (MAD) of 0.33 eV (B3LYP) and 0.34 eV (B3P86), respectively. However, they can accurately predict the excitation energies for states with covalent character (corresponding to group II and I bands). The MAD for group II (B3LYP: 0.05 eV; B3P86: 0.05 eV) and I bands (B3LYP: 0.12 eV; B3P86: 0.12 eV) are significantly smaller. The BLYP outperforms B3LYP and B3P86 for group III band (MAD: 0.09 eV), but has a worse performance for group II (MAD: 0.15 eV) and I (MAD: 0.13 eV) bands. Comparison of the lowest-lying excited states for polycyclic cinnolines with those of the corresponding PAH analogues, the first excited states of polycyclic cinnolines mainly result from n→π₀* transitions. Therefore, in non-polar solvents, the spectra of some polycyclic cinnolines exhibit an additional absorption band at longer wavelengths.     

New relativistic ANO basis sets for transition metal atoms

New basis sets of the atomic natural orbital (ANO) type have been developed for the first, second, and third row transition metal atoms. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive and negative ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies, electron affinities, and excitation energies for all atoms and polarizabilities for spherically symmetric atoms. These calculations include spin-orbit coupling using a variation-perturbation approach. Computed ionization energies have an accuracy better than 0.2 eV in most cases. The accuracy of computed electron affinities is the same except in cases where the experimental values are smaller than 0.5 eV. Accurate results are obtained for the polarizabilities of atoms with spherical symmetry. Multiplet levels are presented for some of the third row transition metals.     

Electronic and cationic states of 2-methylpropene (isobutene) studied by VUV absorption,scattered electron spectroscopy and AB initio multireference configuration interaction calculations

VUV (6.2–9 eV) and electron scattering spectra (1–9 eV) have been recorded for 2-methylpropene (isobutene). Also, electronic states of the molecule, including the ground state and cationic states, have been investigated using ab initio multi-reference configuration interaction calculations. Some Koopmans-type in the UV photoelectron spectrum are reassigned and a number of shake-up states computed. In the electronic spectrum, Rydberg excited have been assigned and a second valence excited state (σ π*) located within about 1 eV of the V(ππ*) state. The experiments show, and theory confirms, that the Rydberg R(π3s) state has a positive electron affinity. Some interesting correlations between ionisation energies, energies of shake-up state electronic excitation energies are identified.     

Excitation energies, electron affinities and ionization potentials of the transition metals V, Cr and Mn

 Configuration interaction calculations were carried out for neutral ground and excited states and positively and negatively ionized states of the V, Cr and Mn atoms. Energy convergence with respect to systematic expansion of both the one-electron and configuration bases was investigated for valence correlation. Contributions from core electrons to the differential correlation energies and relativistic effects were evaluated separately. Assuming additivity of these contributions, excitation energies, electron affinities and ionization potentials of the atoms were obtained. All calculated values were in excellent agreement with the observed values within a deviation of 0.056 eV except for the electron affinity of the V atom, which had a calculated value 0.110 eV larger than the experimental value. Received: 9 August 2000 / Accepted: 26 October 2000 / Published online: 3 April 2001     

Resonant vibrational excitation and de-excitation of CO(v) by low energy electrons

Integral cross sections and rate coefficients for vibrational excitation of the excited carbon-monoxide molecule, via the (2)Pi shape resonance in the energy region from 0 to 5 eV have been calculated. Cross sections are calculated by using our recently measured cross sections for the ground level CO excitation and the most recent cross sections for elastic electron scattering, applying the principle of detailed balance. Rate coefficients are calculated for Maxwellian electron energy distribution, with mean electron energies below 5 eV. By using extended Monte Carlo simulations, electron energy distribution functions (EEDF) and rate coefficients are determined in nonequilibrium conditions, in the presence of homogeneous external electric field. Nonequilibrium rates are calculated for typical, moderate values of the electric field over gas number density ratios, E/N, from 1 to 220 Td. Maxwellian and nonequilibrium rate coefficients are compared and the difference is attributed to a specific shape of the electron energy distribution functions under considered conditions.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

Excited electronic states of the cyclic isomers of O2 and SO2

The low-lying electronic states of O3 and SO2 in their bent and cyclic isomers up to about 10 eV are calculated using the multireference configuration interaction (MRCI) method with a standard Gaussian correlation consistent polarized triple-zeta (cc-pVTZ) basis set. The vertical excitation energies, electron configurations, and oscillator strengths of these states are reported. The molecular orbital structures and excited states of the cyclic isomers are discussed in relation to the bent ones. Coherent anti-Stokes Raman spectroscopy (CARS) schemes for detecting the synthesis of the cyclic isomers are suggested.     

Theoretical prediction of the electronic excited states and resonance Raman intensities in formamide from coupled cluster calculations

Electronic excitations and the resonance Raman spectrum of formamide were obtained from ab initio electron correlation calculations using the equation of motion coupled cluster (EOM-CCSD) method. Interpretation of the UV spectrum on the basis of calculated vertical excitation energies and oscillator strengths accounts for all experimental bands previously assigned. Our assignment, however, suggests an additional Rydberg band at about 7.4 eV which may be hidden under the main absorption. We also show that the Rydberg states appear pairwise, corresponding to n and π hole states, respectively. Using analytic derivative techniques, derivatives of the excited state energies with respect to normal coordinates of the ground state were calculated. Approximate resonance Raman intensities have been determined.     

The Rydberg Nature And Assignments Of Excited States Of The Water Molecule

We report ab initio theoretical calculation on 32 excited states of H₂ O found to lie below 11.7 eV. Of the eight states observed experimentally, the average discrepancy between theoretical and experimental excitation energies is 0.1 eV. We find that the excited states can each be characterized as arising from an excitation to a Rydberg orbital. Our results indicate that the ? and F? states are both 3d-like excited states rather than one 3d state and one 4s state as previously assumed and similarly for the two Rydberg series joining onto ? and F?. The nsa₁ Rydberg series is found to have a quantum defect of 1.38. joining onto the Ã(¹B₁ state. We have assigned the 9.81 eV transition observed by electron impact as the 1b₁ – 3pb₁ excitation to a ³A₁ state.     

Approximate density matrices and Husimi functions using the maximum entropy formulation with constraints

The entropy of an electronic system is defined in terms of the Husimi function, a nonnegative distribution function in phase space. The Husimi function is calculated by maximizing the entropy subject to the constraints that the Husimi function give a Gaussian convolution of the desity when integrating over the momentum coordinates and that its second moment with respect to momentum give a sum of Gaussian convolutions of the density and the kinetic energy density. The result is compared with the Wigner function. Equations are given for calculating the density matrix from the Husimi function. The resulting equation for the exchange energy requires a difficult numerical integration. An alternate method is used to obtain the density matrix from an approximate partially collapsed Husimi matrix that gives the maximum entropy Husimi function as its diagonal. The results are exact for the harmonic oscillator ground state. Exchange energies calculated for H and the He isoelectronic series through C⁺⁴ show slight improvements over those calculated using a maximum entropy Wigner function.