Configuration Interaction Scheme Research Articles

On-Site Correlation in Narrow Band Materials

ABSTRACTWe present the results of a recently developed approach where the interplay between the itinerant and localized character of electrons in narrow band materials is described by adding on-site correlation effects to a realistic band calculation: the single particle band states are treated as mean field solutions of a multi-orbital Hubbard Hamiltonian and the many-body term associated with localized e-e interaction is described in a configuration-interaction scheme. Quasi-particle states of nickel and CuGe03 have been calculated and compared with spectroscopical results.

Generalized doubly symbolic formulation for integral-driven direct configuration interaction method

A direct configuration interaction (CI) scheme using the generalized double symbolism both for the external space and for the internal space is proposed in an integral-driven context. The reason why the double symbolism is used in the present formulation is that the main target is in investigating large molecular systems. The integrals, configuration state functions, and energy expressions are systematically classified in terms of the orbital labels and their mutual relations. Various types of CI wavefunctions can be set up flexibly. The resulting structure of integral processings in the sigma vector construction is complicated. The number of unique loop types for two-electron integrals is 1325. Because the parallel architecture is gaining importance in the recent computational platforms, the parallelism is also addressed.

Retardation long-range potentials between two helium atoms.

The retardation long-range potentials between two 1${\mathrm{}}^{1}$S (or 2${\mathrm{}}^{3}$S) helium atoms are calculated. The complex dynamic multipole polarizabilities of 1${\mathrm{}}^{1}$S and 2${\mathrm{}}^{3}$S states of helium are obtained through a variation-perturbation approach with B-spline and Slater-type basis functions in a configuration-interaction scheme. They are used to calculate the retardation long-range potentials. The retardation coefficients are examined. Their relative magnitudes are different for different systems. The possibility of an excited state of helium dimer from the 1${\mathrm{}}^{1}$S--2${\mathrm{}}^{3}$S ${\mathrm{He}}_{2}$ state is estimated. \textcopyright{} 1996 The American Physical Society.

Theoretical investigations of proton transfer reactions in a hydrogen bonded complex of cytosine with water

The potential energy functions of the electronic ground as well as the lowest ππ* and nπ* excited singlet states of the most stable hydrogen bonded complex of cytosine with water was theoretically investigated along the proton transfer (PT) reaction coordinate. The full geometry optimization was performed along the PT reaction path. In the geometry optimization, the Hartree–Fock method and the configuration interaction scheme with single excitations was used. The energy calculations at the optimized geometries were performed with the complete-active-space self-consistent-field (CASSCF) method and with second-order perturbation theory, employing the CASSCF wave function as the reference state (CASPT2), as well as with the Moller–Plesset second-order theory (MP2) for the ground state. It was found that the cytosine:water complex is stable in the amino-oxo form against the PT reaction which leads to the imino-oxo tautomeric form on the ground as well as on the excited PE surfaces. An efficient nonradiative decay channel of electronically excited cytosine resulting from nonadiabatic interactions between the ground and excited singlet states along the reaction coordinate leading to the prefulvenic form was identified. It is argued that both the above mentioned effects under the normal conditions (neutral aqueous solution, room temperature) are responsible for remarkable stability of cytosine in its ‘‘native’’ amino-oxo form against any damage that may result from exposure to UV radiation.

Theoretical investigations of the excited-state intramolecular proton transfer reaction in N-substituted-3-hydroxypyridinones

Abstract The potential energy functions of the electronic ground state, as well as the lowest n π ∗ and ππ ∗ excited singlet states of 3-hydroxy-4-pyridinone and 3-hydroxy-2-methyl-4-pyridinone, have been theoretically investigated along the proton transfer (PT) reaction coordinate. The full geometry optimization has been performed along the PT reaction path. In the geometry optimization, the Hartree-Fock approximation and the configuration interaction scheme with single excitations have been employed. The energy calculations at the optimized geometries have been performed with the complete-active space self-consistent field (CASSCF) method followed by second-order perturbation theory calculations, employing the CASSCF wave function as the reference. We found that the near-degeneracy between the ππ ∗ and n π ∗ excited singlet states, which is removed upon methyl substitution, might be the factor which differentiates the two systems with respect to the excited state intramolecular PT reaction. A simple vibrational model has been proposed for investigation of the dynamics of the process.

Theoretical study of the electronic spectrum of antimony oxide employing relativistic effective core potentials

Potential energy curves and electric dipole transition moments between different electronic states are computed for the antimony oxide molecule employing a relativistic configuration interaction scheme including the spin–orbit coupling interaction. Comparison is made with available experimental data as well as with the corresponding results which were recently reported for the isovalent BiO. A full core relativistic effective core potential proves to be quite effective in describing the antimony inner shells, thereby reducing the amount of computations considerably relative to an all-electron CI treatment. The calculated bond lengths re for the X1 2Π1/2 ground state and C 2Σ−1/2 excited state agree to within 0.01 Å of the respective measured values and good agreement is also found for the vibrational frequencies ωe of a large number of SbO states. The theoretical treatment tends to underestimate transition energy Te values, typically by 1000–2000 cm−1, reflecting the fact that all excited states have more open shells in their leading configurations than does the ground state itself. On the basis of the present calculations it has been possible to confirm a number of earlier assignments for the SbO upper states and also to aid in the experimental detection of several new transitions involving various a 4Π and b 4Σ− species which were not known at the time this work was begun. Theoretical values for the radiative lifetimes of the v′=0 levels of each of the above electronic states have also been obtained, and they are found to agree within at least a factor of 2 in most cases with the recent experimental values obtained by Fink, Shestakov, and co-workers. The lone exception found to date is for the B 2Σ+ state, but it is noted that nonadiabatic interactions between it and the b1 4Σ−1/2 state, as already discussed in an earlier review by Rai and Rai, could be at least partially responsible for this result.

Oscillator strengths for some systems with the ns2np ground-state configuration. III. Indium isoelectronic sequence

For pt. II see ibid., vol. 26, p.1403 (1993). Configuration interaction gf values for transitions between the 2P0 and 2S, 2D states of some low-lying configurations are reported for the indium isoelectronic sequence up to Ba VIII. As in previously investigated aluminium and gallium sequences, we employ a self-consistent-field method to generate one-electron orbitals. The method includes relativistic effects albeit in an approximate way and the configuration interaction scheme accounts for correlation effects. Comparison with other theoretical or experimental data is difficult due to a severe shortage of such data; nevertheless in most cases fair agreement is found for those that are available.

Theoretical study of many‐body effects in the photoelectron spectra of unsaturated hydrocarbons

AbstractA theoretical investigation on the core and valence photoelectron spectra of unsaturated hydrocarbons of increasing complexity, ethylene, trans‐butadiene, and trans‐hexatriene, has been performed in order to analyze the role of the most important many‐body effects on the spectral features and the evolution of these effects along the series. The capability of various configuration interaction (CI) schemes to interpret both the core and the valence ionization satellite structures has been pointed out. The 3h‐2v(π)‐1p and 2h–1p CI schemes employed, together with an accurate choice of the basis set and the explicit inclusion of the relaxation, has proven to be very useful tools for this kind of study, being sufficiently accurate to explain the most important correlation features and extendible, at the same time, to longer chain systems. © 1994 John Wiley & Sons, Inc.

On the vibronic structure of the absorption spectra of radical cations of some polycyclic aromatic hydrocarbons

The vibronic structure of electronic absorption spectra of four polyacenic radical cations is investigated by means of quantum chemical calculations. We use the semiempirical quantum consistent force field/π electron method (QCFF/PI) augmented by a configuration interaction (CI) scheme that includes all excited configurations having at most one electron in the originally empty molecular orbitals and the ab initio restricted open shell Hartree–Fock (ROHF) method. Displacement parameters for the totally symmetric modes are calculated for different electronic transitions and the resulting Franck–Condon structure is compared with the experimental spectra. The analysis reaffirms the initial interpretation of the absorption spectrum of the cation of naphthalene and reinterprets the recently observed spectrum of the cation of anthracene. First ever analysis of the absorption spectrum of the radical cation of pyrene and perylene is given. For the former, we demonstrate that the unusually large frequency value of the highest ag mode active in the strong absorption band of astronomical interest (443.8 nm) is due to vibronic coupling. For the latter, a resonance vibronic coupling mechanism between manifolds of the 1 2B3g and 1 2B2g states is suggested to explain the doublet structure of the origin of the transition to the latter state.

Partial valence-band spectra of Fe in Cd1-xFexSe.

We have studied the partial valence-band spectrum of Fe in ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se by exploiting the resonant enhancement of the Fe 3d-derived features at the 3p-3d excitation threshold. Two resonance energies of 53.6 and 55.5 eV were detected by performing constant-initial-state measurements. The resonances correspond to transitions from the 3${\mathit{p}}^{6}$3${\mathit{d}}^{6}$ $^{5}$D ground state of the ${\mathrm{Fe}}^{2+}$ ion to 3${\mathit{p}}^{5}$3${\mathit{d}}^{7}$ final states with ${(}^{5}$P${,}^{5}$F) and $^{5}$D symmetry, respectively. By taking difference spectra between energy-distribution curves measured on and off resonance, we obtained partial Fe 3d-derived valence-band spectra that turned out to be quite different for the two resonance energies. In order to understand this difference and to derive ground-state properties from the valence-band spectra of the highly correlated Fe 3d system, a full-fledged configuration-interaction calculation for a [${\mathrm{FeSe}}_{4}$${]}^{6\mathrm{\ensuremath{-}}}$ cluster was performed.Taking the differences in coupling strength of the direct photoemission channels and the two core-excitation resonances into account, these model calculations reproduce the salient features of the partial valence-band spectra quite well. From this model calculation we obtain, among other things, a value for the Fe 3d correlation energy of about 7 eV. The ground state of Fe in ${\mathrm{Cd}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$Se turns out to be describable in terms of 83% of the \ensuremath{\Vert}${\mathit{d}}^{6}$〉 configuration and 17% of the \ensuremath{\Vert}${\mathit{d}}^{7}$L〉 configuration where an electron has been transferred from the ligand (L) to the 3d shell. The effective number of electrons on the Fe atoms is thus calculated to be 6.16. To obtain an independent estimate of the correlation energy we also measured the Fe 2p core lines and modeled the spectrum with a calculation using again the configuration-interaction scheme in the cluster approximation. The best agreement between model and spectrum holds for a correlation energy of 5.5 eV, which is significantly smaller than the value derived from the valence-band spectra.

Dynamic correlation for biorthogonal valence bond reference states

The use of biorthogonal valence bond reference functions in evaluating the correlation energy is investigated. Since the method is not variationally bound some care must be taken in defining the reference state to ensure that the variational bound is not violated, some discussion is given to this matter. The procedure adopted here is a matrix element driven configuration interaction scheme. To reduce the computational labour involved, a configuration selection criterion is introduced. The method is tested through its application to the symmetric stretching of HF, H2O, (2 B 1) NH2 and the singlet-triplet gap in CH2. Comparison is made with other methods, including full CI. The results show that the current method is quite promising.

A comparative study of the satellite structures in the photoelectron spectra of the Ne, Ar and Kr isoelectronic hydrides

The satellite structures relative to the outer and inner valence ionizations of the Ne isoelectronic hydrides have been calculated employing the 3h-2v-1p configuration interaction (CI) scheme and the stability of the results for HF has been tested using the more extended 4h-3v-2p CI approach. The spectra obtained are well comparable with the experimental ones, allowing assignment for the various structures. These results and those previously obtained for the third and fourth row hydrides have been employed for a comprehensive analysis of the satellite structures in these molecules, aimed at a detailed examination of trends down the columns or across the rows. Although the satellites are dominated by similar effects, some different features are present because of the interplay of the quasidegenerate effects of the type found in the noble gases, and the interaction with the antibonding orbitais, which causes a considerable configuration mixing. Evidence is found for the minor importance of the outer valence satellites with respect to the inner valence ones in all molecules examined.

Approximate VB-MO schemes for excitation gaps in Hubbard models

The excitation gaps in the singlet and triplet manifolds for finite Hubbard models in one, two and three dimensions have been obtained using different approximate configuration interaction (CI) schemes, as a function of the correlation strength, by using valence bond (VB) functions constructed over the molecular orbital (MO) basis. These are compared with numerically exact results and it is found that the scheme in which all particle hole excitations below a given threshold are included is the method of choice. The excitation energies are well reproduced, in trend as well as magnitude, particularly when the threshold equals the bandwidth of the corresponding noninteracting system.

Ab initiopseudopotentials for Hg through Rn

Quasirelativistic and nonrelativistic energy adjusted ab initio pseudopotentials for the elements Hg through Rn are presented together with corresponding optimized valence basis sets. Core-valence correlation is accounted for by semiempirical polarization potentials. Corrections to the point charge repulsion in the core-nucleus interaction for subsequent molecular calculations are also provided. The reliability of the pseudopotential method is demonstrated in atomic test calculations for electron affinities, excitation and ionization energies as well as spin-orbit splittings by comparison with nonrelativistic, quasirelativistic and relativistic all-electron data. Results obtained by means of two quasirelativistic configuration interaction schemes that include spin-orbit coupling are compared with experimental data.

Analysis of the CIPSI/DCCI approach to characterize the HF AND F 2 single bond

The aim of the present work is to account for the main differential correlation contributions occurring during the bond breaking process of HF and F 2 molecules in an accurate and inexpensive way. Starting from the dissociation-consistent configuration interaction (DCCI) scheme by Goddard and co-workers the corresponding contributions are evaluated within the framework reported by Malrieu and co-workers, namely configuration interaction by perturbation with multiconfigurational zeroth-order wavefunction selected by iterative process (CIPSI). In addition, the DCCI scheme has been improved by introducing the dispersion effects associated with the valence MOs adjacent to the bond. The present results show a good agreement with the full Cl data available. Including f functions in the one-electron basis sets, the calculated r e ( D e) values, 1.757 a 0 (5.98 eV) and 2.668 a 0 (1.64 eV) for HF and F 2, reflect a clear trend towards the corresponding experimental data.

Application of the time-dependent Hartree grid method to inelastic molecular scattering problems

A time-dependent Hartree grid wavepacket propagation method (in which each degree of freedom is represented by a numerical grid, and evolved according to one-dimensional mean field equations) is successfully utilized to calculate S-matrix elements for collinear atom—Morse oscillator scattering. The possibility of developing a convergeable configuration-interaction scheme based upon zeroth-order time-dependent Hartree evolution is briefly discussed.

A method of incorporating quadruple correction in the scheme of multi-reference singly and doubly excited configuration interaction ? a CSF based coupled pair approximation

We develop an approximate size consistent method within a framework of the multi-reference configuration interaction scheme. The Rayleigh-Schrodinger perturbation theory is employed with a specific selection of the unperturbed part of the electronic Hamiltonian. The second order energy is obtained by a set of equations similar to the quasidegenerate variational perturbation theory of Cave and Davidson. The approximate fourth order energy is obtained by solving a set of equations similar to the coupled electron pair approximation (CEPA). The method has been tested for two simple systems, BeH2 and N2, and the results are quite encouraging.

Multiphoton spectroscopy of doubly excited, bound, and autoionizing states of strontium.

We present a theory attempting an interpretation of existing data on three- and four-photon ionization of Sr in the wavelength range 557--575 nm and at 532 nm. Two-photon resonances with bound excited states and three-photon resonances with doubly excited autoionizing states are studied. ac Stark shifts and broadening of resonances, as well as singlet-triplet transitions, are shown to yield interesting new information on atomic structure. The absorption of a fourth photon above the threshold leads to excited final ionic states, with autoionizing states having served as intermediate three-photon resonances. The calculation is based on a configuration-interaction scheme, with singlet-triplet mixing taken into account either through jl coupling or phenomenologically by adjustment to some aspects of the data. The apparatus of resonant multiphoton theory is combined with the above scheme. Depending on the quantity in question, the agreement between theory and experiment ranges from good to semiquantitative.

Relativistic configuration interaction calculations for polyatomics: Applications to PbH2, SnH2, and GeH2

A relativistic configuration interaction scheme is described for polyatomic molecules containing heavy atoms. In this method first complete active space MCSCF followed by large scale configuration interaction calculations are carried out. The natural orbitals generated in the large scale CI are then used in the relativistic CI (RCI) calculations, which include the spin–orbit integrals. The spin–orbit integrals are obtained using large Gaussian basis sets, with the operator expressed as a difference of relativistic effective core potentials, and then transformed over the natural orbitals. The transformed integrals are included as one-electron matrix elements in the RCI. This procedure thus takes into account both electron correlation and spin–orbit effects. The method is applied to the spin–orbit states derived from the three low-lying states of PbH2, SnH2, and GeH2 (1A1, 3B1, and 1B1). The spin–orbit mixings of the 1A1 and 3B1(A1) states in the RCI wave functions of PbH2 and SnH2 were found to be quite significant. For PbH2 this mixing lowers the 1A1 state by 1308 cm−1 while the 3B1(A1) is raised by 1371 cm−1 with respect to the 3B1 state without the spin–orbit splitting. The dipole moments of all the three radicals reveal that PbH2 has the largest dipole moment of the three. The electronic states of GeH2 and SnH2 are similar [1A1(A1)−3B1(A1):Te=23.1 kcal/mol for GeH2, Te=23.8 kcal/mol for SnH2], but the electronic states of PbH2 differ [1A1(A1)–3B1(A1):Te=41 kcal/mol] from their lighter analogs in that the splittings of the excited states are considerably higher. The Mulliken population analyses of the CI natural orbitals reveal that this is primarily a result of the relativistic stabilization of the 6s orbital of the lead atom due to the mass–velocity contraction. The geometries of the A1 component of the 3B1 state are altered to a considerable extent by the spin–orbit term for both PbH2 and SnH2.

Cas SCF/CI calculations on electronic states of Br 2 and Br 2+

MC SCF (complete active space SCF) followed by first-order configuration interaction (FOCI) calculations are carried out on sixteen electronic states of Br 2 and six electronic states of Br 2 + as a function of internuclear distance. Spin-orbit interaction was introduced for some of the electronic states using a relativistic configuration interaction scheme. Spectroscopic properties are calculated for bound electronic states. Our calculations enable confirmation of experimental assignment of a number of electronic spectra below 60000 cm −1 for Br 2. These calculations also predict properties of a few electronic states which are yet to be observed. The calculations of Br 2 + enable reinterpretation of the photoelectron spectra of Br 2 and the assignment of the observed bands. Our relativistic CI calculations show that the 2Π u ( 1 2 ) component of the first excited 2Π u state undergoes avoided crossing with 4Σ − u ( 1 2 ) state leading to substantially different vibrational frequency for this state in comparison with 2Π u ( 3 2 ). Spectroscopic properties of six electronic states of Br 2 + are calculated which are yet to be observed.