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.     

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.     

AB initio effective spin—orbit operators for use in atomic and molecular structure calculations. Results for carbon and silicon

Ab initio effective spin-orbit operators for carbon and silicon are derived from relativistic effective core potentials based on Dirac—Fock wavefunctions. Transferability of these operators to electronic states other than the one used in the original derivation is treated by calculating spin—orbit splittings of various neutral and ionic atomic states.     

SCA calculations of the inner shell ionization with Dirac-Fock electronic wave functions

The theory of inner shell ionization for arbitrary atomic shells is reviewed. Emphasis is onL- andM-shells in order to show how the proper screening formalism entering the electronic form factor affects the ionization probabilities. The radial wavefunctions in the form factor are computed as relativistic Hartree-Fock orbitals for both bound and continuum states. The continuum orbitals were evaluated in theV(N–1) potential with correct exchange. These results are then compared with the previous ones using screened hydrogen-like wavefunctions and also with the experimental data in some cases.     

Generalized relativistic effective core potentials for superheavy elements

The generalized relativistic effective core potentials (GRECPs) for calculations of electronic structure and physical-chemical properties of compounds containing superheavy elements (Z ≥ 104) are presented. Features of accounting for the finite nuclear size effects which are unusually large for superheavy elements are discussed in details. Accuracy of the GRECPs is analyzed in atomic calculations compared to all-electron studies with the Dirac-Coulomb-Breit Hamiltonian. Applications of the GRECP method in molecular and cluster calculations are surveyed.     

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.     

Atoms in molecules: beyond Born–Oppenheimer paradigm

This contribution presents the first atoms in molecules study that goes beyond the Born–Oppenheimer paradigm employing the newly developed two-component quantum theory of atoms in molecules (TC-QTAIM). The LiH, LiD, and LiT systems containing quantum instead of clamped hydrogen nuclei are used as typical examples. The computational analysis that is done on non-adiabatic wavefunctions derived from the fully variational multicomponent molecular orbital approach (FV-MC-MO) results in hydrogen atomic basins without any clamped nucleus. The topological analysis of the Γ-field, the field that replaces the usual one-electron density used in the orthodox topological analysis, reveals delicate differences among the considered systems. The calculation of basin properties also demonstrates that the TC-QTAIM differentiates among atomic basins containing isotopes. Since the nuclear dynamics is contained intrinsically in non-adiabatic wavefunctions, the nuclear contribution to both topological analysis and basin properties naturally emerges from the TC-QTAIM analysis resolving the long-standing obstacle of consistent incorporation of nuclear dynamics within the context of the orthodox QTAIM. Also, a similar analysis is done on non-adiabatic wavefunctions describing excited instead of ground nuclear vibrations of the considered systems demonstrating the fact that TC-QTAIM is capable of being employed for both ground and excited nuclear vibrational states.     

The einstein a-coefficient of spontaneous emission: a relativistic calculation in the Heisenberg representation

We present a simple approach to the relativistic calculation of the rates of spontaneous emission starting from the Heisenberg picture formula for the power radiated by a charged particle undergoing acceleration, and evaluate atomic decay rates using relativistic Dirac-Coulomb wavefunctions. The spin of the electron, embedded in its relativistic wavefunction, is shown to correctly provide the two polarization states of the emitted radiation. We discuss selection rules and calculate the Hydrogen 2P → 1S transition rate, among others, to be Γ=(6.2650±0.0007)×10⁸ s^?1 in good agreement with the full field theory calculation as well as with experiment.     

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.     

Ab initio relativistic self-consistent-field (RSCF) wavefunctions for the diatomics Li2 and Be2

RSCF wavefunctions are calculated using the formalism of the authors. The results essentially agree with the non- relativistic calculations as expected because relativistic effects are negligible for these light atom diatomics.     

Relativistic molecular wavefunctions: XeF2

A new method is presented to calculate binding energies and eigenfunctions for molecules, using the relativistic Dirac hamiltonian. A numerical basis set of four component wavefunctions is obtained from atom-like Dirac-Slater wavefunctions. A discrete variational method has been developed and applied to the linear XeF₂ molecule.     

Structural and electrostatic properties of atoms and functional groups using AIM theory: Saturated organics with one electronegative atom

Atoms in molecules (AIM) theory is used to determine the properties of functional groups within 73 saturated linear and branched molecules with at most one electronegative atom. The group properties found rigorously in AIM theory and computed in this study are energy, volume, exposed surface area, extent of electron density, charge, dipole moment and polarizability of the group. Properties of atoms and groups within small molecules are presented. Averaged values for group definitions subdivided by their first-bonded neighbors are also presented. Small variability in properties is seen for hydrogen, fluorine, oxygen, nitrogen and larger groups containing the latter three atoms. Greater variability exists within the database of alkyl group values, and the range of these quantities is discussed. Exposed surface area calculations using AIM theory are explained and related to van der Waals (vdW) radii methods.     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

两类双粒子函数建造的n电子波函数的扩展及其应用

讨论了具有辛群对称性的一类n电子波函数Ψ_(n, s_1, s_2)=NQ_+~s1(ξ) multiply from t=1 to 2 a_t~+_(a_t)G~+(ξ, r, v_(r+1)|0>的性质. 这类函数是两类双粒子函数建造的n电子波函数的扩展. 它们既适用于闭壳层, 也适用于开壳层体系. 用此类函数计算了Li_2、LiH-_2、CH+_3、OH~-等体系. 结果表明, 这类函数能较好地描述电子和关作用。     

Molecular orbitals for excited states of atoms and molecules

A method is described for calculating SCF wavefunctions for excited electronic states of atoms and molecules. The orthogonality conditions with the ground state wavefunction and the underlying excited states wavefunctions are introduced in the SCF process in a simplified form.     

Quantum wavepacket ab initio molecular dynamics: generalizations using an extended Lagrangian treatment of diabatic states coupled through multireference electronic structure

We present a generalization to our previously developed quantum wavepacket ab initio molecular dynamics (QWAIMD) method by using multiple diabatic electronic reduced single particle density matrices, propagated within an extended Lagrangian paradigm. The Slater determinantal wavefunctions associated with the density matrices utilized may be orthogonal or nonorthogonal with respect to each other. This generalization directly results from an analysis of the variance in electronic structure with quantum nuclear degrees of freedom. The diabatic electronic states are treated here as classical parametric variables and propagated simultaneously along with the quantum wavepacket and classical nuclei. Each electronic density matrix is constrained to be N-representable. Consequently two sets of new methods are derived: extended Lagrangian-QWAIMD (xLag-QWAIMD) and diabatic extended Lagrangian-QWAIMD (DxLag-QWAIMD). In both cases, the instantaneous potential energy surface for the quantum nuclear degrees of freedom is constructed from the diabatic states using an on-the-fly nonorthogonal multireference formalism. By introducing generalized grid-based electronic basis functions, we eliminate the basis set dependence on the quantum nucleus. Subsequent reuse of the two-electron integrals during the on-the-fly potential energy surface computation stage yields a substantial reduction in computational costs. Specifically, both xLag-QWAIMD and DxLag-QWAIMD turn out to be about two orders of magnitude faster than our previously developed time-dependent deterministic sampling implementation of QWAIMD. Energy conservation properties, accuracy of the associated potential surfaces, and vibrational properties are analyzed for a family of hydrogen bonded systems.     

Electronic states of titanium monoxide. An ab initio study

Ab initio calculations have been performed to determine predominant configurations and CI wavefunctions of the observed electronic states of the TiO molecules. Insight in the structure of these states is gained owing to an analysis of electronic populations of the orbitals. Calculated energies and spectroscopic properties are in generally good agreement with experimental data. The wavefunctions are used to calculate values for the experimentally unknown dipole moments in each of the states.     

A new method to generate spin-orbit coupled potential energy surfaces: effective relativistic coupling by asymptotic representation

A new method has been developed to generate fully coupled potential energy surfaces including derivative and spin-orbit coupling. The method is based on an asymptotic (atomic) representation of the molecular fine structure states and a corresponding diabatization. The effective relativistic coupling is described by a constant spin-orbit coupling matrix and the geometry dependence of the coupling is accounted for by the diabatization. This approach is very efficient, particularly for certain systems containing a very heavy atom, and yields consistent results throughout nuclear configuration space. A first application to a diatomic system is presented as proof of principle and is compared to accurate ab initio calculations. However, the method is widely applicable to general polyatomic systems in full dimensionality, containing several relativistic atoms and treating higher order relativistic couplings as well.