Carbazole and trinitrofluorenone: an ab initio investigation of ionization potentials,electron affinities and excited states

Minimal basis set SCF calculations are reported for the ground states and positive and negative ions of carbazole and tirnitrofluorenone. For carbazole, wavefunctions for several low-lyng excited states have also been obtained. Methods for surmounting convergence difficulties for these large systems are discussed. Relaxation effects in the calculations of excitations energies are considered and found to be significant. Calculated energies are compared to experimental results.     

INDO-SCF and CI calculations on the trans-cis isomerization of azomethane in the ground state and in excited states

INDO-SCF calculations followed by CI calculations with inclusion of multiply, excited configurations were carried out to obtain potential energy curves for isomerization in the ground state and in some low-lying excited states of azomethane. The SCF wavefunctions are analyzed with the aid of newly defined bond characters providing a connection between the chemical concepts of bonds, lone-pairs, etc. and molecular orbital theory. Two different pathways for isomerization are considered and by comparison of the calculated results with experimental data it is concluded that this reaction proceeds in the ^1,3 (nπ*) states via rotation of both methyl groups around the NN double bond.     

Variational wavefunctions for low-lying excited states

The multiconfiguration method based on the generalized Brillouin theorem is well suited to optimize orbitals in variational wavefunctions for low-lying excited states of a given symmetry. Such wavefunctions are constrained to be orthogonal to and noninteracting with the wavefunctions for all lower states of the same symmetry. Test calculations were performed on the lowest excited ¹S state of Be. For a Hartree-Fock ground state wavefunction, singly excited configurations were insufficient to describe the lowest excited state, and triply excited configurations had to be added. For multiconfiguration ground state wavefunctions, however, singly excited configurations gave good results.     

On the lower excited electronic states of biacetyl

An ab initio SCF and CI study has been carried out for the ground and electronically excited states of biacetyl (CH₃COCOCH₃). The second absorption band in the 4.40 eV region has been assigned to a ¹A_g → ¹B_g nπ^* transition The character of the lower-lying states has been analyzed in terms of the CI wavefunctions.     

Fe and Ni AB initio effective potentials for use in molecular calculations

We present effective potentials to replace the Ar core electrons of Fe and Ni. These effective potentials are obtained from ab initio ground state wavefunctions of Fe and Ni and are tested by comparing with ab initio SCF calculations for excited states of Fe, Fe⁺, Fe²⁺, Fe³⁺, Ni, Ni⁺, Ni²⁺, and the FeH⁺ molecule.     

Iterative diagonalization in the state-averaged multi-configurational time-dependent Hartree approach: excited state tunneling splittings in malonaldehyde

An iterative block Lanczos-type diagonalization scheme utilizing the state-averaged multi-configurational time-dependent Hartree (MCTDH) approach is introduced. Combining propagation in real and imaginary time and using a set of initial seed wavefunctions corresponding to excitations via the different components of the dipole moment vector, the scheme can favorably be used to selectively compute vibrational states which show high intensities in vibrational absorption spectra. Tunneling splitted vibrational states in double well systems can be described particularly efficient employing an increased set of seed wavefunctions which includes symmetric and anti-symmetric wavefunctions simultaneously. The new approach is used to study the tunneling splittings of the vibrationally excited states of malonaldehyde. Full-dimensional multi-layer MCTDH calculations are performed and results for the tunneling splittings of several excited vibrational states can be obtained. The calculated tunneling splittings agree reasonably well with available experimental data. Order of magnitude differences between tunneling splittings of different vibrationally excited states are found and interpreted.     

On the ordering of the ionization energies in N2: A MC SCF study of near-degeneracy effects

Single configuration SCF wavefunctions yield poor results for the order and relative energies of low-lying icnic states of N₂. A multi-configurational SCF (MC SCF) model which takes account of the near degeneracy of a small number of strongly and weakly occupied orbitals corrects the errors of the SCF approach. MC SCF results for N₂ predict the correct ordering and give reasonably accurate results for the three lowest ionization potentials.     

Broken orbital symmetry and the description of valence hole states in the tetrahedral [CrO4]2− anion

The localization of ligand-based valence holes in the tetrahedral complex ion [CrO₄]^2? in a crystalline environment is studied by SCF calculations on the hole states, with progressively less restrictions on the spatial symmetry of the molecular orbitals. The final wavefunctions are obtained by constructing, from the symmetry broken SCF solutions, wavefunctions that exhibit again the proper transformation properties under the operations of T _d . The crystal environment of the [CrO₄]^2? anion is represented by a point charge model. In contrast with the situation for core hole states, the projection afterwards into T _d symmetry is important. The final ionization energies, which are obtained from projected C _3v adapted SCF solutions, are reduced considerably (?3 eV) with respect to the T _d ΔSCF results, but the ordering of the states has not changed essentially. The calculated ionization energies compare favourably with results of XPS experiments on Na₂CrO₄. The evaluation of the energies of projected symmetry broken SCF solutions requires the calculation of hamiltonian matrix elements between determinantal wavefunctions built from mutually non-orthogonal orbital sets. An efficient method for the calculation of such matrix elements is presented.     

Configuration interaction study of the oscillator strenghts for the A1--- A1 and A1--- A1 transitions of the water molecule

Oscillator strengths for transitions between the ¹A₁ ground state of water and its ¹A₁ and ¹A₁ excited states are computed employing two different theoretical approaches. In one series of calculations a common orthonormal one-electron basis is employed for all of the above states, while in the other type of treatment two different, mutually non-orthogonal, sets are used; the multireference single- and double-excitation (MRD CI) method is employed in each case, with configuration selection, to generate the various electronic wavefunctions. It is found that the use of ground-state SCF MOs leads to poor convergence in the wavefunctions of the (Rydberg-type) ¹A₁ and ¹A₁ excited states and consequently also for the corresponding --- and --- f-values; this behavior is seen to be closely related to the near degeneracy of the two excited states, each of which is a mixture of the 3a₁ → 3sa₁ and 1b₁ → 3pb₁ configurations. Analogous computations with the ¹B₁¹b₁ → 3sa₁ MOs show much better convergence properties, and the resulting f-values compare well with what is obtained when state-specific orbital sets are employed separately for ground and excited states and non-orthonormal techniques are applied to compute the desired transition moments. These results tend to confirm previous findings which indicate conceptual and computational advantages for the calculation of excited-state wavefunctions and properties within the context of a state-specific theory. They also show that although the goal of eliminating the dependence of MRD CI calculations on the choice of MO basis is very nearly approached for energy quantities, it is less satisfactorily achieved for other properties, especially when the existence of nearly degenerate electronic states is a critical factor.     

Constraint Variational Calculations on Excited States

The difficulties of the SCF and MCSCF calculations on excited states have been reviewed. Three constraint variational methods are then developed which can perform the SCF and MCSCF calculations on excited states in the scheme of the generalized Brillouin theorem method. The proper constraints and the ways to incorporate the constraints into the variational calculations on excited states have been studied and the comparison with other approaches have been accessed.     

Approximate second order method for orbital optimization of SCF and MCSCF wavefunctions

A quasi-Newton method involving a diagonal guess orbital hessian with iterative updates has been proposed recently by Almlof for the optimization of closed shell self-consistent field (SCF) wavefunctions. The technique is extended in the present work to more general wavefunctions, ranging from open shell SCF through multiconfigurational SCF. A number of examples are presented to show that convergence for closed and open shell SCF rivals conventional direct inversion in the iterative subspace (DIIS). For multiconfigurational SCF wavefunctions, the method presented here requires more iterations than an exact second order program, but since each iteration is substantially faster, leads to a more efficient overall program. Received: 15 August 1996 / Accepted: 22 January 1997     

Structures and spectra of Na(NH3) n=1,2

Geometric structures and the energies for the ground and several excited electronic states of a sodium atom bound with one or two ammonia molecules are presented. All self consistent field (SCF) calculations are performed with extended basis sets. Geometry optimization and one electron properties have been performed within the SCF approximation. Excited states have been calculated with the multi-configuration SCF (MCSCF) technique. This system may be viewed as a precursor to solvation in a macroscopic system. The excited state calculations provide important information for spectroscopic studies of these complexes.     

SCF scheme for excited states and analysis of the orbital relaxation effect for H2O and FNO

An SCF scheme for excited states of closed-shell systems based on the direct minimization technique is discussed. The utility of the scheme is tested for several excited states of H₂O. The contribution of various tyeps of optimization of orbitals occupied in the excited state is discussed using the example of H₂ O and FNO. It was found that relaxation of doubly occupied orbitals always gives a significnat contribution to the lowering of the excited state energy in the SCF process. Unexpectedly, on the other hand, optimization of the excited orbital in many cases gave negligible results.     

Calculation of excited singlet and triplet state polarizabilities using the CNDO/S CI method. An application to naphthalene

A procedure is outlined for the calculation of molecular static electric polarizabilities in excited singlet and triplet states using the ”finite perturbation theory“ in conjunction with the CNDO/S CI method. Numerical results for the ground and the three lowest excited singlet and triplet states of naphthalene are presented. It turns out that the generalized Hellmann-Feynman theorem is approximately valid for the CNDO/S CI wavefunctions and that triplet and singlet state polarizabilities in states of the same symmetry may strongly differ.     

Overtone intensities in resonance Raman scattering

A model calculation of resonance Raman scattering tensors has been carried out for a diatomic molecule with a harmonic potential for the ground state and a linear repulsive potential for the excited state. Expressions for scattering tensors have been obtained by using a series of recurrence formulas induced from the Green function of the nuclear hamiltonian of the repulsive potential of the excited state and nuclear wavefunctions for the harmonic potential. The relative scattering intensities of overtones depend on the gradient of the repulsive potential curve and are interpreted in terms of the overlap integrals between nuclear wavefunctions of upper and lower states.     

Linear response calculation of potential energy curves of BH

The multiconfiguration time-dependent Hartree–Fock (MC TDHF ) approximation is applied to study the excited states of the BH molecule. The potential energy curves and spectroscopic properties of the excited states are analyzed. The MC TDHF results are compared to similar MC SCF calculations for individual excited states. © 1994 John Wiley & Sons, Inc.     

Consistent generalization of the Møller-Plesset partitioning to open-shell and multiconfigurational SCF reference states in many-body perturbation theory

The Møller-Plesset partitioning of the many-electron Hamiltonian is generalized for arbitrary open-shell and multiconfigurational SCF reference states. The method has been initially implemented at the second and third orders for two-configuration generalized valence bond reference wavefunctions in which only two electrons are correlated. Potential curves for the hydrogen molecule, lithium hydride and the helium dication agree excellently with full CI results.     

Superconvergent Perturbation Theory for an Anharmonic Oscillator

A computationally facile superconvergent perturbation theory for the energies and wavefunctions of the bound states of one-dimensional anharmonic oscillators is suggested. The proposed approach uses a Kolmogorov repartitioning of the Hamiltonian with perturbative order. The unperturbed and perturbed parts of the Hamiltonian are defined in terms of projections in Hilbert space, which allows for zero-order wavefunctions that are linear combinations of basis functions. The method is demonstrated on quartic anharmonic oscillators using a basis of generalized coherent states and, in contrast to usual perturbation theories, converges absolutely. Moreover, the method is shown to converge for excited states, and it is shown that the rate of convergence does not deteriorate appreciably with excitation.