Multireference Double Excitation Configuration Interaction Research Articles

Photodissociation of water in the à band revisited with new potential energy surfaces

Theoretical calculations on the photodissociation of water in the first absorption band have been used to test the accuracy of three available potential energy surfaces for the first excited state of water: the well-known coupled electron pair approximation potential of Staemmler and Palma [Chem. Phys. 93, 63 (1985)], and two new multireference double excitation configuration interaction surfaces: the Dobbyn–Knowles surface (unpublished), and the Leiden surface [R. van Harrevelt and M. C. van Hemert, J. Chem. Phys. 112, 5777 (2000)]. Exact quantum mechanical calculations, using the wave packet approach, have been performed for J″>0, where J″ is the initial rotational state of the water molecule. The cross section was found not to depend strongly on the rotational state, so that it is reasonable to compare calculated cross sections for J″=0 with experimental room temperature cross sections. Small and simple corrections were applied to the potential energy surface to improve the agreement between theory and experiment for the cross section of H2O. Spectra for D2O and vibrationally excited water molecules calculated with all three corrected potential energy surfaces were in good agreement with experiments. A comparison between calculated OH(X) or OD(X) vibrational distributions, and recent kinetic energy release measurements of the H or D atoms produced in the 157.6 nm photodissociation of water and its isotopomers [Yang et al., J. Chem. Phys. 113, 10597 (2000)], however, suggests that the Leiden surface is more accurate than the two other surfaces.

Resonance enhanced multiphoton ionization spectroscopy of the NCI molecule: 1Σ Rydberg states studied by 2-photon excitation from the a1Δ state

Three 1Π Rydberg states of the NCI molecule, accessed from the NCl a1 ΔA state, have been investigated by multiphoton ionization spectroscopy. NCl was prepared from the Cl + N3 reaction and the excited 1Π states were observed via the 2-photon resonance enhancements they provide in the multiphoton ionization spectrum of NCl a1 Δ. Assignment of the initial and final electronic states associated with each band was achieved by rotational band contour simulations, least-squares fitting of the resolved rotational structure, recording spectra with linearly and circularly polarized radiation and recording spectra in the N35Cl+ and N37Cl+ mass channels. The Π+/Π− character of each excited state as well as the dominant electronic configuration at spectroscopically accessible bond lengths was established by multireference double excitation configuration interaction (MRDCI) calculations.

A quantum chemical investigation of possible intermediates in the reaction of the amidogen and hydroperoxyl radicals

The reaction NH2+HO2→products, a reaction of atmospheric interest, has been studied using ab initio molecular orbital calculations with extended basis sets [6-311++G** and 6-311++G(2df,2pd)], and a variety of methods accounting for electron correlation such as second order Mo/ller–Plesset perturbation theory (MP2) with all electrons, quadratic configuration interaction singles and doubles with triples correction [QCISD(T)], complete active space [CAS(8,8)], and multireference double excitation configuration interaction (MRDCI). Also, the performance of density functional (DFT) calculations has been investigated. In the present study, all stationary points on various potential energy surfaces giving rise to different products, HNO+H2O, NH2O+OH, NH3+O2, H2O2+NH, and HNOO+H2, have been optimized and characterized by their Hessian matrix. Amine oxide and dihydroxyamine have been found to be the precursors for HNO formation. In addition, the paper attempts to explain the experimental finding, nonobservation of OH⋅ during photolysis of ammonia, and it demands new experiments with spectroscopic identification of OH radicals.

Resonance enhanced multiphoton ionization spectroscopy of the NF molecule: 1,3Φ 3d and 4d Rydberg states

The (3dδ)1,3Φ and (4dδ)1,3Φ Rydberg states of NF have been investigated by multiphoton ionization (MPI) spectroscopy. These states were observed as two-photon resonances in an overall (2+1) MPI process from NF a1Δ produced from the F+N3 reaction. Ab initio calculations performed at the multireference double excitation configuration interaction level showed that the excited Φ states were of Rydberg character with configurations of ...1π45σ22π1(3dδ)1 and ...1π45σ22π1(4dδ)1. The 3Φ←a1Δ two-photon transitions were found to derive their intensities from spin–orbit and spin-uncoupling interactions in the 1Φ3, 3Φ4, 3Φ3, and 3Φ2 upper states. Analysis of the rotationally resolved bands, using a model which includes these factors, allowed the spin–orbit constant, aπ, for the 2π valence orbital to be derived as (159.0±1.0) cm−1. Rotationally resolved envelopes recorded for the (3dδ)1Φ, v′=0, 1←a1Δ, v″=0 and (3pπ)1Σ+, v′=0←a1Δ, v″=0 (2+1) NF MPI bands, could be simulated reasonably well assuming a Boltzmann rotational distribution for the a 1Δ state at ≊180 K. Experiments showed, however, that this was not a true measure of the initial state distribution because of predissociation or perturbation effects in the resonant intermediate state. Assignments for other two-photon resonant NF MPI bands observed in this work are also suggested.

On some structural properties of various electronic states of the hydroxonium ion

Calculations have been carried out for several excited electronic states of the protonated water molecule the hydroxonium ion H3O+ at the level of highly correlated, multireference double-excitation configuration-interaction (MRD-CI) computations for several potential energy profiles of the system. It was found that different structural geometries exist for the ground and for the excited electronic states and that such geometries are very helpful for a quantitative interpretation of previous mass spectrometric fragmentation patterns. The general features of the umbrella motion in several electronic states are described for the title system and their importance for the analysis of the above spectra is shown for the first time. The possible extension of the present study to analyze charge-exchange and direct inelastic collision experiments in molecular beams is briefly outlined.

Theoretical study of electron spin resonance parameters: H2CN and H2CO+

The hyperfine structure of the two isoelectronic molecules H2CN and H2CO+ in their electronic ground state (X 2B2) is studied. The influence of the atomic orbital (AO) basis sets, of the correlation treatment, and of the equilibrium geometry on the obtained hyperfine properties is investigated. It is found that the multireference double excitation-configuration interaction (MRD-CI)/BK treatment in which an MRD-CI wave function is corrected by a modified BK method yields equivalent results to quadratic CI [QCISD(T)], coupled cluster single doubles [CCSD(T)], or Brueckner doubles [BD(T)]. Uncertainties in the equilibrium geometries are found to be the major source for discrepancies between theoretically and experimentally determined isotropic hyperfine coupling constants (hfccs). For the heavier centers, the calculated values of the isotropic hfccs agrees nearly perfectly with experimental values (≊1%–2%). The calculated values for the hydrogens are too low, but using the equilibrium structure suggested by Yamamoto and Sato [J. Chem. Phys. 96, 4157 (1992)], the best estimate deviates by less than 3%.

Ab initioMRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. III. Me2N?NO2 decomposition of dimethylnitramine in a large crystalline environment

Recently we extended our strategy for MRD-CI (multireference double excitation-configuration interaction) calculations, based on localized/local orbitals and an “effective” CI Hamiltonian, for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystalline or other solid environment. Our technique begins with an explicit quantum chemical SCF calculation for a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized, and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-CI calculations are then carried out for breaking a bond in the reference molecule. This method is completely general in that the space treated explicitly, as well as the surrounding space, may contain voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. Dimethylnitramine is the smallest prototype of the energetic R2N—NO2 nitramines, such as the 6-member ring RDX or the 8-member ring HMX. Decomposition of energetic compounds is initiated in the solid by a breaking of the target bond. Thus, it is crucial to know the difference in energy between breaking a bond in an isolated energetic molecule versus in the molecule in a solid. In the present study, we have carried out MRD-CI calculations for the Me2N—NO2 dissociation of dimethylnitramine in a dimethylnitramine crystal. The cases we investigated were one dimethylnitramine molecule (surrounded by 53 and 685 neighboring dimethylnitramine molecules represented by multipoles), three dimethylnitramine molecules, and three dimethylnitramine molecules (surrounded by 683 neighbors). All multipoles were cumulative atomic multipoles up through quadrupoles. The MRD-CI calculations on dimethylnitramine required large numbers of reference configurations from which were allowed all single and double excitations.

Ab‐Initio MRD‐CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment. II.H3C—NO2 decomposition of nitromethane in a nitromethane crystal with voids

AbstractRecently we extended our strategy for MRD‐CI (multireference double excitation‐configuration interaction) calculations based on localized/local orbitals and an “effective” CI Hamiltonian for molecular decompositions of large molecules to breaking a chemical bond in a molecule in a crystal or other solid environment. Our technique involves solving a quantum chemical ab‐initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of more distant neighbors. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD‐CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD‐CI calculations are carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have voids, defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We previously applied this procedure successfully to the H3CNO2 bond dissociation of nitromethane in a nitromethane crystal with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many molecules have to be represented by more distant multipoles. The results indicated that it took more energy to dissociate the H3CNO2 bond when the nitromethane molecule was in the crystal than it did to dissociate that bond in the free nitromethane molecule. In this present study we have investigated the effect of voids (both in the nitromethane molecules treated explicitly in the SCF and those in the environment represented by multipoles) on the calculated H3CNO2 bond dissociation energies.

Multireference coupled cluster and multireference configuration interaction studies of the potential surfaces for deprotonation of NH+4

Protonation/deprotonation reactions are represented by H++B⇄HB+. The ionization potential of H (13.6 eV) is higher than that of B for organic and most inorganic molecules (it is 10.166 eV for NH3), and the separated pair H+B+ will be lower in energy than the closed-shell pair H++B. The reaction path involves, therefore, an avoided crossing, and its theoretical study requires multideterminant methods. The reaction with B=NH3 (or R1R2R3N) is of interest in several fields, and its study is described here. The multireference coupled-cluster method (MR-CCM) and multireference double-excitation configuration interaction (MRD-CI) were used. At each (H3N---H)+ separation, from 1 to 11 bohr, the ground state MRD-CI energy was optimized with respect to the angle θ between the NH bond in the NH3 group and the C3 axis; MR-CCM and MRD-CI calculations were performed for the two lowest 1A1 states and the lowest 3A1. Two different reference determinants had to be used for the MR-CCM calculations at different regions, but this created no difficulties and the transition was smooth. Close agreement (a few mhartree) was obtained between MRD-CI and MR-CCM results. The avoided crossing, near R(H3N---H)+=4 bohr, is manifested by the rapid change in the CI and coupled-cluster method (CCM) mixing coefficients and by the transition of the NH3 group from pyramidal at small R to planar at large R. The lowest 1A1 state dissociates adiabatically to NH+3(2A1)+H(2S), whereas the single determinant self-consistent field (SCF) function dissociates to NH3(1A1)+H+.

A new computational strategy for ab-initio MRD-CI calculations for breaking a chemical bond in a molecule in a crystal or other solid environment

Abstract Recently we derived, implemented, tested and used successfully a new computational strategy for ab-initio MRD-CI (multireference double excitation-configuration interaction) calculations for molecular decompositions of large molecules and intermolecular reactions of large systems. We carry out the ab-initio SCF for the entire system, then transform the canonical delocalized molecular orbitals to localized orbitals and include explicitly in the MRD-CI only the localized occupied and virtual orbitals in the region of interest, folding the remainder of the occupied localized orbitals into an “effective” CI Hamiltonian. The advantage is that the transformations from integrals over atomic orbitals to integrals over molecular orbitals (the computer time-, computer core- and external storage-consuming part of the CI calculations) only have to be carried out for the localized orbitals included explicitly in the MRD-CI calculations. The challenge arose to extend our MRD-CI technique based on localized/local orbitals and “effective” CI Hamiltonian to the breaking of a chemical bond in a molecule in a crystal (or other solid environment). This past year we have derived, implemented and used successfully a procedure for doing this. Our technique involves solving a quantum chemical ab-initio SCF explicitly for a system of a reference molecule surrounded by a number of other molecules in the multipole environment of yet more further out surrounding molecules. The resulting canonical molecular orbitals are then localized and the localized occupied and virtual orbitals in the region of interest are included explicitly in the MRD-CI with the remainder of the occupied localized orbitals being folded into an “effective” CI Hamiltonian. The MRD-I calculations are then carried out for breaking a bond in the reference molecule. This method is completely general. The space treated explicitly quantum chemically and the surrounding space can have defects, deformations, dislocations, impurities, dopants, edges and surfaces, boundaries, etc. We have applied this procedure successfully to the H3CNO2 bond dissociation of nitromethane with extensive testing of the number of molecules that have to be included explicitly in the SCF and how many further out molecules have to be represented by multipoles. To check the goodness of the model cluster approximation for crystalline nitromethane, we carried out ab-initio crystal orbital (XTLORB) calculations using our POLY-CRYST program. The difference in the XTLORB total energies between the 4 nitromethane molecules/unit cell and the 3 nitromethane molecules/unit cell, ER = E4 − E3 = − 48.0609079 a.u., corresponds very closely to the reduced energy per nitromethane molecule, ER = − 48.06057 a.u., calculated from explicit SCF calculations on the model nitromethane cluster in the multipole field of farther out nitromethane molecules for the model cluster. Thus, the multipole approximation for describing the effect of further out molecules on the SCF cluster energies is quite good.

Wavelength regulation in bacteriorhodopsin and halorhodopsin: A Pariser–Parr–Pople multireference double excitation configuration interaction study of retinal dyes

A Pariser–Parr–Pople (PPP) Hamiltonian is employed to study many-electron excitations in protonated and unprotonated retinal Schiff bases. Excited states are described by a multireference double excitation configuration interaction expansion (MRD-CI) and a simplified perturbational treatment. The effects of electron correlation on the spectra of retinal dyes are analyzed and compared with experimental data. It is shown that the spectra of retinal Schiff bases are much more sensitive to the effects of protonation and charge environment than previously assumed. Based on an analysis of observations the computational results demonstrate that varying counterion distance is the essential mechanism of wavelength regulation in the retinal proteins bacteriohodopsin (BR) and halorhodopsin (HR). Spectral properties of intermediates of the photocycles of BR and HR are predicted and it is shown that available spectroscopic data are compatible with a 13,14-cis model of these cycles. Independent evidence is provided that the quantum yield of photoisomerization in BR is 0.6.

Systematic ab initio configuration-interaction study of alkali-metal clusters. II. Relation between electronic structure and geometry of small sodium clusters.

The quantum-chemical investigation of the electronic and geometrical structure of neutral sodium clusters carried out with the all-electron Hartree-Fock (HF) or effective-core-potential HF followed by multireference double-excitation configuration-interaction (MRD-CI) procedure demonstrates the complete analogy to the electronic properties of ${\mathrm{Li}}_{\mathrm{n}}$ clusters. The general rules determining the electronic properties of small alkali-metal clusters are again clearly confirmed. Under experimental conditions which do not allow strong cluster fragmentation the large abundances of ${\mathrm{Na}}_{8}$ and ${\mathrm{Na}}_{4}$ can be expected.

Ab‐initioMRD–CI calculations on a CNO2 decomposition pathway of nitrobenzene

AbstractTo study molecular decomposition pathways it is necessary to use ab initio multireference determinant–configuration interaction or MCSCF (multiconfiguration SCF) calculations. The MRD–CI (multireference double excitation–configuration interaction technique of Buenker and Peyerimhoff) calculations on the magnified image decomposition pathway of nitrobenzene were carried out using all of the occupied molecular orbitals in the region of the magnified image bond being dissociated, plus all of the virtual orbitals. An effective CI Hamiltonian was used into which were folded the effects of all of the occupied molecular orbitals from which excitations were not allowed. So far we have investigated the lowest 1A1, 3A1, 1A2, 3A2, 1B1, 3B1, 1B2, 3B2 states and are investigating the higher states. Our results show a wealth of structure in the potential energy surfaces for the various electronic states of nitrobenzene as a function of magnified image distance. A number of the states are predissociative and change dominant configuration one or more times along these potential energy surfaces.

Ab initioMRD-CI calculations for the propagation step of cationic polymerization of oxetanes based on localized orbitals

In the propagation step of the cationic polymerization, oxetane reacts with the protonated oxetane formed in the initiation step, with concomitant ring opening of the protonated oxetane. To describe properly bond making or bond breaking, it is necessary to use MC-SCF or CI calculations. We have carried out ab initio MODPOT/VRDDO MRD-CI calculations (by the multireference double excitation–configuration interaction technique of Buenker and Peyerimhoff into which we have also meshed a number of desirable computational options for ab initio calculations on large molecules). The CI calculations were carried out on strictly orthogonalized localized occupied and virtual orbitals in the reaction region, with the remainder of the occupied molecular orbitals being folded into an effective CI Hamiltonian. The calculated potential energy surfaces indicate that a preferred pathway for this reaction resembles an SN2 reaction with the oxygen of the oxetane attacking linearly along the C4O direction of the protonated oxetane and inversion of the hydrogens around the C4 atom.

The low-lying electronic excitations in long polyenes: A PPP-MRD-CI study

A correct description of the electronic excitations in polyenes demands that electron correlation is accounted for correctly. Very large expansions are necessary including many-electron configurations with at least one, two, three, and four electrons promoted from the Hartree–Fock ground state. The enormous size of such expansions had prohibited accurate computations of the spectra for polyenes with more than ten π electrons. We present a multireference double excitation configuration interaction method (MRD-CI) which allows such computations for polyenes with up to 16 π electrons. We employ a Pariser–Parr–Pople (PPP) model Hamiltonian. For short polyenes with up to ten π electrons our calculations reproduce the excitation energies resulting from full-CI calculations. We extend our calculations to study the low-lying electronic excitations of the longer polyenes, in particular, the gap between the first optically forbidden and the first optically allowed excited singlet state. The size of this gap is shown to depend strongly on the degree of bond alternation and on the dielectric shielding of the Coulomb repulsion between the π electrons.

Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators.

A no-pair formalism employing external-field projection operators correct to second order in the potential is used to calculate the 1s energies of one-electron atoms and ground-state properties of the bromine and silver atoms in the framework of the multireference double-excitation configuration-interaction (MRD-CI) method. It is found that the relativistic two-component method that has been used reproduces the one-particle energies of the Dirac equation to order (Z\ensuremath{\alpha}${)}^{3}$. The operator is bounded from below and can be used variationally in relativistic electron-structure calculations of many-electron atoms and molecules. The relativistic correction to the total energy recovers 97% of the relativistic correction of the Dirac-Hartree-Fock (DHF) result in the case of the bromine atom and more than 99% in the case of the silver atom. The relativistic correction of the ionization potential of silver has been calculated to be 0.47 eV at the CI level, in good agreement with DHF results, the correlation contribution in the relativistic case being 0.42 eV. The remaining discrepancy of the absolute value of 6.85 eV (DHF 6.34 eV) to experiment (7.57 eV) is attributed to basis-set deficiencies. The corresponding CI value of the electron affinity (relativistic CI value 1.05 eV, nonrelativistic 0.90 eV) is in much better agreement with experiment (1.30 eV). It is found that correlation contribution and relativistic effects are nonadditive.

Configuration interaction studies of low-lying valence and Rydberg states of NS

Using a better than double-zeta-plus-polarization basis set, the multireference-double-excitation-configuration-interaction (MRD-CI) method has been employed to calculate the potential curves for the X 2Π, a 4Π (unobserved), b 4Σ− (unobserved), B 2Π, 2Φ (unobserved?), A 2Δ, C 2Σ+ (Rydberg), H 2Π, I 2Σ+, and J 2Σ+ (Rydberg) states of the NS radical. Except for the B′ 2Σ+ state, which is not found in our calculations, all the calculated Te and re values for experimentally observed states are found to be in good agreement with experiment, whereas the calculated ωe’s are only satisfactory. Arguments have been advanced to identify the experimental observed B′ 2Σ+ state as the calculated 2Φ state. The radiative lifetime for the v′=0 level of the C 2Σ+ state has been calculated to be about 30 ns, indicating the level predissociates since the experimental radiative lifetime is only 6.5 ns.

Low-lying electronic states of Ben clusters (n = 7, 10, 13) and of the Be7H system

Self-consistent-field (SCF) calculations have been performed by means of a pseudopotential (PP) technique on medium-size Be n clusters ( n = 7, 10, 13). Correlation effects have been taken into account through multireference double-excitation configuration-interaction (MRD CI) procedure. Particular attention has been paid to the existence of Be clusters with many nearly degenerated states of singlet and triplet spin multiplicity. The SCF ordering of these states is frequently reversed in CI. Planar and non-planar Be clusters show comparable high stabilities caused by a strong sp hybridization. Two sections of the potential energy surface for the interaction of a H atom with the Be 7 (7,0) cluster have been determined. Two regions of low energy found in this energy surface: one inside and the second outside the cluster border, are separated by an energy barrier. The CI results, indicating the directly overhead position as the absolute minimum of the surface, are in qualitative agreement with previous SCF studies on similar systems. The modifications of the cluster geometry (shrinkage or relaxation) caused by the interaction with the H atom in the directly overhead position are found to be very small.

The bond nature of alkaline-earth homonuclear metal clusters investigated with pseudopotential CI method

The electronic stucture of Be l , Mg m and Ca n ( 1⩽ 7, m and n ⩽ 5) metal clusters has been investigated by means of an ab initio pseudopotential method followed by multireference double-excitation configuration interaction (PP MRD CI). Two completely different situations arise on going from Be to heavier alkaline metals. The sp hybridization, which is effective in the Be case, completely disappears when aggregates of Mg and Ca are considered. The potential energy curves relative to Be, Mg and Ca clusters exhibit a very shallow minimum at large distances while a second deeper minimum is characteristic of some Be clusters. This inner minimum is generated by the large interaction of atomic p orbitals at an internuclear separation close to the BeBe distance present in the Be crystal. The bond in Be clusters largely depends on the geometrical arrangement which directly influences the possible sp hybridisation. Very small Be planar structures are always less favored with respect to clusters containing the tetrahedral unit as a part of the whole structure. However, this situation is changed when larger planar clusters are considered, and the highest binding energy per atom (12.0 kcal/mole) from all clusters considered in this work was found for the triplet ground state of the planar Be 7(D 6h) cluster.

Theoretical dipole derivatives for HCN and DCN

Hartree–Fock–Roothaan self-consistent-field (SCF) and multireference double-excitation configuration interaction (MRD–CI) methods have been used to compute the potential and dipole moment surfaces for the HCN molecule, from which a variety of molecular properties, such as equilibrium bond distances, force constants, equilibrium dipole moment and derivatives with respect to the normal coordinates, and integrated intensities for HCN and DCN, have been derived and compared with available experimental data. Satisfactory agreement is generally found between the MRD–CI and the experimental results, e.g., the calculated dipole derivatives with respect to the stretching normal coordinates are, with experimental values given in parentheses, −8.6 (±4.5) and −88.9 (±88) esu for HCN and −22.6 (±20) and −61.1 (±66) esu for DCN. Nevertheless, the calculated dipole derivatives with respect to the bending normal coordinate (80.1 and 46.4 esu, respectively, for HCN and DCN) are found to be much larger than the corresponding experimental values of 61 and 32 esu, discrepancies which would appear to be far too large to be attributed entirely to deficiencies in the present theoretical treatment.