Multi-reference Coupled Pair Approximation Research Articles

Ab initio calculation of the electronic structures of the Φ3 ground and Φ5 excited states of CoH

The electronic structures and the spectroscopic constants of the electronic ground Φ3 and low-lying Φ5 electronic excited states of the CoH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI)+Davidson’s correction (Q) calculations and size-consistent multireference coupled pair approximation (MRCPA) calculations. Calculations were performed under C∞v symmetry using Slater-type basis functions. The electronic ground state was confirmed to be the Φ3 state. It was found that at least four reference configurations were needed to describe the ground Φ3 state correctly at the MR-SDCI+Q level, while the Φ5 state can be described well by one reference configuration, namely, the Hartree-Fock configuration. Larger dynamical electron correlation for the low-spin Φ3 state than that for the high-spin Φ5 state is discussed. Spectroscopic constants, i.e., equilibrium bond lengths (re), harmonic frequency (ωe), and excitation energy, obtained by the MR-SDCI+Q method showed good correspondence with experimental values. MRCPA calculations gave a slightly shorter value for re than experimental values, but improved ωe and the excitation energy bringing them very close to experimental values.

Theoretical study of the electronic structure of the lower states of the [Cr2Cl9]3− and [Mo2Cl9]3− ions

The electronic structure of the lower states of a trigonal Cr3+ pair and Mo3+ pair, which occur in the Cs3M2Cl9 crystal (M=Cr,Mo), were studied by theoretical calculations carried out according to several methods: multireference singly and doubly excited configuration interaction, second-order configuration interaction, and multireference coupled-pair approximation. We employed a model of a [M2Cl9]3- anion embedded in a cage of point charges, which were arranged so as to simulate the anion in the crystal. The model core potential was utilized, where the relativistic effect was included for Mo. Results of the Cr complex showed that there were no direct bonds between the Cr metals. The lower electronic spectra of the [Cr2Cl9]3- ion were interpreted in terms of the electronic spectra of [CrCl6]3-. The lowest state of simultaneous excitation in both metals was considered. The [Mo2Cl9]3- ion exhibited a single direct bond between the metals. Reflecting this single bond, the observed singlet-triplet splitting was much larger than that in the case of Cr and the calculated splitting was in good agreement with the observed one. We account for the electronic spectra of the [Mo2Cl9]3- complex, which exhibited quite different features in the electronic excitation spectra in comparison with those of the Cr complex.

Theoretical study of bending and symmetric stretching vibrational levels of the lowest five quintet and two triplet states of FeH 2

Adiabatic potential surfaces of the lowest two triplet states and the lowest five quintet states of FeH 2 were calculated using ab initio multi-reference singly and doubly excited configuration interaction plus Davidson's type correction. Multi-reference coupled pair approximation was applied to obtain more accurate term energies of the triplet states. In contrast to the quintet states, which are known to be linear, the lowest two triplet states are strongly bent. Vibrational analyses of both quintet and triplet states were carried out. We discuss the effect of non-adiabatic coupling on the bending vibrational levels of 5 B 2 and (2) 5 A 1 through a conical intersection.

A theoretical study on lower electronic states of CoN

In order to identify the ground state of CoN, we carried out calculations of multi-reference single and double excitation configuration interaction with Davidson-type correction and multi-reference coupled pair approximation (MRCPA). MRCPA predicts that 1Σ + is the ground state of CoN. The 5 Δ state lies only 0.223 eV above 1Σ +. Internuclear equilibrium distance, harmonic frequency, and rotational constants of 1Σ + agree well with experimental results.

Structure and bonding of the (C6H6)+ 2 radical

To elucidate the relative stability of various structures of the benzene dimer cation radical, (C6H6)+ 2 in its ground and low-lying excited states, ab initio complete active space self-consistent field (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations were performed. Full optimization was performed at the CASSCF level for various structures of the dimer cation, followed by MRSDCI and MRCPA calculations. It was found that the global minimum of the cation is at a slipped C2h sandwich structure but there are some other sandwich structures with almost the same stability, being within about kcal mol−1. T-shape structures are less stable than the sandwich structures, by more than 5 kcal mol−1 by MRCPA calculations. Low lying electronic excited states in various structures are also discussed.

Theoretical study of the TiC molecule: clarification of the ground state

The electronic structure of the TiC molecule was examined using three types of multi-reference single- and double-excitation configuration interaction (MRSDCI) calculations with highly extended basis sets. Multi-reference coupled pair approximation (MRCPA) was applied after the MRSDCI calculations that included core—valence and core—core correlation in addition to the valence correlation (v-c-c CI). From the results of the most accurate calculation with MRCPA (v-c-c CPA) it was concluded that a 1Σ+ state is the ground state, despite previous calculations that suggested a 3Σ+ state with a 1Σ+ state lying only slightly above it. The 1Σ+ state is more highly correlated than the 3Σ+ state, and it was found that use of a size-consistent method is necessary to predict the relative stability accurately. The study evaluated the spectroscopic constants and considered the effect of the core (Ti 3p) correlation on these parameters. By taking the core correlation effect into account, the estimation of the dissociation energy (D e) was improved dramatically; D e obtained through v-c-c CPA was 4.457eV for the 1Σ+ ground state, which agrees well with the experimental value (the latest being 4.35 ± 0.31 eV).

Ab initio study of the lower few states of FeH: Application of the multireference coupled pair approximation

Multireference coupled pair approximation(4) [MRCPA(4)] was applied to describe the ground state and the lower excited states of FeH. This study demonstrates that the a 6Δ state is 0.27 eV above the ground state, X 4Δ, which is in good agreement with the observation (0.25 eV). The ground state is much more highly correlated than the a 6Δ state and the use of the size-consistent method is important to predict the relative stability accurately. In addition to the above results, spectroscopic data of the second Δ,4 the lowest Π,4 the lowest Φ4, the lowest two Π6, and the lowest Σ+6 states are reported. The calculated excitation energies of the lowest Σ+6 state and the second Δ4 state are in good agreement with results of experiment. The total energies of the lowest Δ4, Π,4, Δ6, Π6 and Σ+6 states are in the order of Δ4<Π4<Δ6<Π6<Σ+6 which supports what was anticipated previously.

Ab-initio study on low-lying states of the TiSi molecule

The electronic structure of the TiSi molecule was examined using two types of multireference single and double excitation configuration interactions with highly extended basis sets, one including valence correlation and the other including valence and core–valence correlation. A multireference coupled-pair approximation (MRCPA) was further applied to the latter. The calculations suggest a 5Δ ground state, and the lowest excited state is 3Π and is only slightly (0.12 eV as estimated by MRCPA) above the ground state. The spectroscopic constants of the low-lying 1Δ, 3Δ, 1Π, 5Π, and 7Σ+ states as well as the 5Δ ground state and the 3Π excited states were evaluated, and we found that the molecule has only a weak σ bond and that six of the eight valence electrons essentially do not contribute to the bonding. The bonding nature of TiSi in these states is discussed in comparison with the TiC molecule.

Theoretical study of low-lying electronic states of TiCl and ZrCl

Low-lying electronic states of TiCl and ZrCl were investigated by the complete active space SCF (CASSCF), multi-reference singly and doubly excited configuration interaction (MRSDCI), and multi-reference coupled pair approximation (MRCPA) calculations using the model core potential (MCP) method. Relativistic effects were incorporated in the MCP and basis sets for Zr at the level of Cowan and Griffin’s quasi-relativistic Hartree–Fock method. The 4Φ state was found to be the ground state of TiCl, whereas the 2Δ state was the ground state of ZrCl at all levels of calculation. Two low-lying excited states were very close in energy to the ground state. The excited 4Σ−and 2Δ states of TiCl were higher than the ground state by 0.102 eV and 0.458 eV, respectively, and the excited 4Φ and 4Σ− states of ZrCl were higher by 0.094 eV and 0.110 eV, respectively, at the MRCPA level. The calculated values of re(2.319 Å) and ωe(382 cm−1) for the ground 4Φ state of TiCl are quite close to the values of re(2.351 Å) and ωe(383 cm−1) for the ground 2Δ state of ZrCl. The values of re, ωe, Be, and αe are reasonably comparable to the observed values for both TiCl and ZrCl.

Multireference coupled-pair approximation study of the CuSi molecule

The electronic structure of the CuSi molecule was examined using the multireference coupled pair-approximation (MRCPA) following multireference single and double excitation configuration interaction calculations. We found the ground state to be the 2Π state, and we evaluated the bond length, dissociation energy, vibrational frequency, and dipole moment for the 2Π ground state and for low-lying 4Σ− and 2Δ excited states. The dissociation energy of the 2Π ground state by MRCPA is 2.13 eV, which agrees well with the experimental value of 2.26 eV. The inclusion of higher excitations by MRCPA significantly improves the description of the bonding and the accuracy of the spectroscopic constants.

Multi-reference coupled pair approximation (MRCPA) calculations for the ground state of the ArI 2 complex

We performed multi-reference coupled pair approximation (MRCPA) calculations as well as single-reference CPA (SRCPA) calculations for the ground state of the ArI 2 complex using relativistic model core potentials which included major relativistic effects. The localized natural orbital (LNO) set approach was used to calculate the correlation energy. The T-shaped and linear isomers had almost the same binding energies. MRCPA calculations gave a potential surface on which the T-shaped minimum was lower than the linear minimum by 9 cm −1, while SRCPA calculations predicted that the linear and the T-shaped isomers were almost degenerate within 2 cm −1. The MR approach preferred the T-shaped geometry. The vibrational frequencies for the van der Waals stretch mode in the T-shaped and linear isomers were calculated to be 64 and 46 cm −1, respectively.

Theoretical spectroscopic constants of the GaN molecule

Fourth-order multi-reference coupled pair approximation (MRCPA-4) calculations were performed to predict spectroscopic constants of the gallium nitride (GaN) diatomic molecule. The calculations showed that the ground state is 3Σ− but that the 3Π state is low lying and separated from the former by 0.5 eV. The contribution of the correlations among the Ga 3d semi-core electrons was found to be crucial for a quantitative description of the molecule.

A CSF-based multi-reference coupled pair approximation

Using the newly developed multi-reference coupled pair approximation program code, the adiabatic potential curves of the ground states of F2, As2 and As2+ were calculated. Computed spectroscopic constants of these molecules were found to be in good agreement with experimental values. The resulting binding energy of As2 (3.86 eV) was compared with the experimental value of 3.99 eV [15] and the best multi-reference configuration interaction value (3.58 eV) reported previously by the present authors. The calculated first adiabatic ionization potential of As2 (9.67 eV) was found to be in good agreement with the experimental result.

A CSF-based multireference coupled pair approximation

MRCPA (multireference coupled pair approximation) is formulated by the use of the wave operator formalism and Rayleigh-Schrodiner perturbation theory with special selection of the unperturbed part of the electronic Hamiltonian. By considering super molecule, it is shown that the theory is size consistent with the help of the new formalism. The method has been tested for three simple systems, H2O, FH, and O2.