Calculation of molar Kerr and Cotton-Mouton constants of azines as aza-substituted benzenoid hydrocarbons

For the case of aza substitution within coupled Hartree-Fock -electron perturbation theory, we consider the effect of substituents on double refraction of alternant hydrocarbons in transverse electric and magnetic fields. The calculated values of the Kerr and Cotton-Mouton constants in the azine series agree well with experimental data.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 28, No. 2, pp. 124–130, March–April, 1992.     

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.     

Variational-Perturbation theory in the LCAO-MO method for closed-shell molecules

Using the variational principle, equations have been obtained for density matrix of molecules with the external perturbation of the common type present. The perturbed wave function was taken as a superposition of the ground and single-excited configurations made of the Hartree-Fock molecular spin orbitals. On the basis of these equations a series of variants of static perturbation theory have been worked out for the ground and excited states of closed-shell molecules.     

Excited states of the benzyl radical

The CI method is used in the -electron approximation with orbitals for closed and open shells to calculate the properties of excited doublet states with allowance for all singly excited configurations and some doubly excited ones, and also for the first quartet and sextet states, which are calculated in the one-configuration approximation via the open-shell theory. The energies and transition moments agree satisfactorily with the available experimental evidence. A classification and assignment is given for the excited terms. Truncation of the complete set of singly excited configurations greatly distorts the calculated spectrum. Inclusion of doubly excited configurations in the CI also produces a substantial change in the spectrum; in some cases it alters the order of adjacent terms. Conversion in CI from basis closed-shell orbitals to open-shell ones produces a considerable lowering of all terms in the spectrum. As in the case of triplet terms for molecules, weakening of electron interaction brings the lowest excited term of the radical closer to the ground-state term. The electron-density and spin-density distributions are calculated for the excited states.     

Delayed Doublet Emission in a Cerium(III) Complex

Doublet emission from open-shell molecules has demonstrated its research and application value in recent years. However, understandings of the photoluminescence mechanism of open-shell molecules are far less than that of closed-shell molecules, leading to challenges in molecular design of efficient doublet emission systems. Here we report a cerium(III) 4-(9H-carbozol-9-yl)phenyl-tris(pyrazolyl)borate complex Ce(CzPhTp)₃ with a new luminescence mechanism of delayed doublet emission, which also represents the first example with metal-centered delayed photoluminescence. The energy gap between the doublet and triplet excited states of Ce(CzPhTp)₃ is reduced by the management of the inner and outer coordination spheres, thereby promoting efficient energy transfer between the two excited states and activating the delayed emission. The photoluminescence mechanism discovered may provide a new way for the design of efficient doublet emission and bring insights into rational molecular design and energy level regulation in open-shell molecules.     

Quantum chemical study of the electronic structure of NiCH2 + in its ground state and low-lying electronic excited states

The electronic structure of NiCH(2) (+), representative of transition metal carbene ions, is investigated by means of several methods of quantum chemistry. The relative stabilities of the four low-lying doublet electronic states ((2)A(1), (2)A(2), (2)B(1), and (2)B(2)) are determined at the coupled cluster singles and doubles level (CCSD) and triples level [CCSD(T) and CCSDT-3] with both a Hartree-Fock and density functional theory (Kohn-Sham) reference. The equation-of-motion coupled cluster for treatment of excited states in singles and doubles approximation (EOM-CCSD) is used to characterize the transition energies from the (2)A(1) electronic ground state to the low-lying doublet excited states. The (2)A(2) and (2)B(1) states are nearly degenerate, found to be separated by 940 cm(-1) at the EOM-CCSD level, in agreement with the CASSCF energy ordering. The (2)B(2) state is calculated to be higher in energy by more than 1.0 eV. The spin purity of the low-lying doublet and quadruplet states described by CCSD calculations based on the unrestricted open-shell Hartree-Fock reference is discussed.     

An application of second-order n-electron valence state perturbation theory to the calculation of excited states

n–electron valence state perturbation theory (NEVPT) is a form of multireference perturbation theory where all the zero-order wave functions are of multireference nature, being generated as eigenfunctions of a two–electron model Hamiltonian. The absence of intruder states makes NEVPT an interesting choice for the calculation of electronically excited states. Test calculations have been performed on several valence and Rydberg transitions for the formaldehyde and acetone molecules; the results are in good accordance with the best calculations and with the existing experimental data.Contribution to the Jacopo Tomasi Honorary Issue     

The shifted scheme in the general-model-space diagrammatic perturbation theory

The shifted scheme of many-body perturbation theory is applied to open-shell states within the framework of the general-model-space theory. Rules for shifting the denominators of folded diagrams. which appear in open-shell perturbation expansions, are given. The finite-order energies in the shifted scheme obtained in two equivalent representations may differ. This happens, for instance, in the case of triplet states. For ³Σ_u⁺ states of the He₂, differences up to 0.07 mhartree have been found in third order. A similar phenomenon is the size inconsistency of the shifted scheme observed by Silver in the ground state of He₂. A possible advantage of the shifted scheme is its faster convergence for excited states.     

New concepts of the mechanism of hydrogen exchange between organic molecules and strong acidic centers

Ab initio calculations of the activation energy of the reaction of hydrogen exchange between the methane molecule and the H₃O⁺ ion in the gaseous phase have been carried out by using Hartree-Fock methods and Moeller-Plesset second order perturbation theory (MP2) methods. The structure of the transition state of this reaction has been found. The interaction of the H₃O⁺ ion with molecules of aliphatic hydrocarbons and amino acids has been studied by the Serniernpirical AMI method.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 7, pp. 1852–1854, July, 1996.     

Excited state geometries within time-dependent and restricted open-shell density functional theories

Singlet excited state geometries of a set of medium sized molecules with different characteristic lowest excitations are studied. Geometry optimizations of excited states are performed with two closely related restricted open-shell Kohn–Sham methods and within linear response to time-dependent density functional theory. The results are compared to wave-function based methods. Excitation energies (vertical and adiabatic) calculated from the open-shell methods show systematic errors depending on the type of excitation. However, for all states accessible by the restricted methods a good agreement for the geometries with time-dependent density functional theory and wave-function based methods is found. An analysis of the energy with respect to the mixing angle for the singly occupied orbitals reveals that some states (mostly [n→π^*]) are stable when symmetry constraints are relaxed and others (mostly [π→π^*]) are instable. This has major implications on the applicability of the restricted open-shell methods in molecular dynamics simulations.     

A finite B-spline basis set for accurate diatomic molecule calculations

A finite basis set particularly adapted for solving the Hartree-Fock equation for diatomic molecules in prolate spheroidal coordinates has been constructed. These basis functions have been devised as products of B-splines times associated Legendre polynomials. Due to the large number of B-splines, the resulting set of eigenfunctions is amply distributed over excited states. This gives the possibility of using these basis sets to calculate sums over excited states, appearing in various orders of perturbation theory. As an illustration, the second-order corrections to the ground-state energy of some atoms and diatomic molecules with closed electron shells have been calculated.     

Use of semiempirical models for calculation of B terms in MCD spectra—III : Pariser-Parr-Pople (PPP) predictions for dications and dianions of pentalene and heptalene

The PPP model is used to predict the MCD spectra of the doubly-charged ions of pentalene and heptalene. The excited states of the 10 π-electron ions are both related to those of naphthalene and exhibit interesting configuration pairing similar to that found in alternant hydrocarbons. Certain aspects of the results are very sensitive to the choice of parameters and to inclusion of doubly excited configurations in the PPP model. Comparison with the so far non-existent experimental data would probably be useful for testing the various proposed versions of the model.     

Electron localization and delocalization in open-shell molecules

Localization and delocalization indices derived in the framework of the quantum Atoms in Molecules theory have recently been used to analyze the electron-pair structure of closed-shell molecules. Here we report calculations of localization and delocalization indices for open-shell molecules at the Hartree-Fock (HF) level. Several simple doublet and triplet radical molecules are studied. In general, interatomic delocalization between bonded atoms is heavily dependent on the order and polarity of the bond. Unpaired electrons also have a significant effect on the interatomic delocalization indices. Indeed, for many radicals, the analysis of the spin components reveals that the interatomic delocalization is very different for alpha and beta spin electrons in many cases. In general, at the HF level, the results can be rationalized in terms of orbital contributions. However, the definition of localization and delocalization indices is completely general, and they could be calculated at any level of theory, provided that the one- and two-electron densities are available.     

Spin-orbit coupling of ππ*-states of aromatic molecules in zero differential overlap approximation

It has been shown that, in the standard -scheme using a 2p_z-AO basis and the principle of zero differential overlap, there are nonzero three-center contributions of one-electron spin-orbit coupling (SOC). Systematic calculations have been performed on the -channel of SOC for condensed and heteroaromatic molecules. Prohibition rules in alternant hydrocarbons make it possible to ignore, in the firstorder approximation, SOC between states with identical alternant parity. It has been shown that SOC of -states in systems with a chain structure is an order of magnitude smaller than in analogous condensed systems. A breakdown of alternant character in heterosubstitution usually reduces the SOC effect.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 1, pp. 17–25, January–February, 1990.     

Note on the ab initio PUHF treatment of open-shell systems

Ab initio projected-unrestricted Hartree-Fock calculations have been carried out on a number of excited and ionic states of the water molecule. Results have been compared with large-scale CI calculations, with IVO calculations, and with those of Mrozek and Golebiewski obtained by the 2 × 2 rotation method applied to orbitals. It is concluded that the PUHF method may provide the most useful alternative to large-scale CI for calculating properties of open-shell systems. But it will not be generally useful for calculating spectral transition energies.     

Coupled cluster methods including triple excitations for excited states of radicals

We report an extension of the coupled cluster iterative-triples model, CC3, to excited states of open-shell molecules, including radicals. We define the method for both spin-unrestricted Hartree-Fock (UHF) and spin-restricted open-shell Hartree-Fock (ROHF) reference determinants and discuss its efficient implementation in the PSI3 program package. The program is streamlined to use at most O(N(7)) computational steps and avoids storage of the triple-excitation amplitudes for both the ground- and excited-state calculations. The excitation-energy program makes use of a Lowdin projection formalism (comparable to that of earlier implementations) that allows computational reduction of the Davidson algorithm to only the single- and double-excitation space, but limits the calculation to only one excited state at a time. However, a root-following algorithm may be used to compute energies for multiple states of the same symmetry. Benchmark applications of the new methods to the lowest valence (2)B(1) state of the allyl radical, low-lying states of the CH and CO(+) diatomics, and the nitromethyl radical show substantial improvement over ROHF- and UHF-based CCSD excitation energies for states with strong double-excitation character or cases suffering from significant spin contamination. For the allyl radical, CC3 adiabatic excitation energies differ from experiment by less than 0.02 eV, while for the (2)Sigma(+) state of CH, significant errors of more than 0.4 eV remain.     

Singly excited bound states in continuum: a time-dependent perturbation approach

Summary Time-dependent coupled Hartree-Fock (TDCHF) scheme has been applied to study the behaviour of bound excited states embedded in the continuum for the negative ions Li^–, F^–, Na^– and Cl^–. The excited states have been obtained from the position of the poles of the dynamic polarizability values which are evaluated for all the ions within and beyond the normal dispersion region. Transition energies and dipole allowed oscillator strengths have been obtained for several transitions which lie in the continuum. Although the excited state functions are extremely diffuse, they show proper asymptotic behaviour and furnish correct number of nodes. Oscillator strengths are found to follow a different trend than observed in normal bound state calculations.