First-order Configuration Interaction Research Articles

MCSCF optimization revisited. II. Combined first- and second-order orbital optimization for large molecules.

A new orbital optimization for the multiconfiguration self-consistent field method is presented. This method combines a second-order (SO) algorithm for the optimization of the active orbitals with the first-order super configuration interaction (SCI) optimization of the remaining closed-virtual rotations and is denoted as the SO-SCI method. The SO-SCI method significantly improves the convergence as compared to the conventional SCI method. In combination with density fitting, the intermediates from the gradient calculation can be reused to evaluate the two-electron integrals required for the active Hessian without introducing a large computational overhead. The orbitals and CI coefficients are optimized alternately, but the CI-orbital coupling is accounted for by the limited memory Broyden-Fletcher-Goldfarb-Shanno quasi-Newton method. This further improves the speed of convergence. The method is applicable to large molecules. The efficiency and robustness of the presented method is demonstrated in benchmark calculations for 21 aromatic molecules as well as for various transition metal complexes with up to 826 electrons and 5154 basis functions.

Effect of electron correlation and shape resonance on photoionization from the S1 and S2 states of pyrazine

In a previous study [T. Horio, T. Fuji, Y.-I. Suzuki, and T. Suzuki, J. Am. Chem. Soc. 131, 10392 (2009)], we demonstrated that the time-energy map of photoelectron angular anisotropy enables unambiguous identification of ultrafast S(2)(ππ*)-S(1)(nπ*) internal conversion in pyrazine. A notable characteristic of this map is that the forbidden ionization process of D(0)(n(-1)) ← S(2)(ππ*) gives a negative photoelectron anisotropy parameter. In the present study, we elucidate the mechanism of this process by calculating the photoionization transition dipole moments and photoelectron angular distribution using the first-order configuration interaction method and the continuum multiple scattering Xα approximation; these calculations at the S(0) equilibrium geometry reproduce the observed anisotropy parameters for D(0) ← S(2) and D(0) ← S(1) ionizations, respectively. On the other hand, they do not reproduce the small difference in the photoelectron anisotropy parameters for the D(1)(π(-1)) ← S(2) and D(0) ← S(1) ionizations, both of which correspond to removal of an electron from the same π* orbital in the excited states. We show that these ionizations are affected by the ka(g) shape resonance and that the difference between their photoelectron anisotropy parameters originates from the difference in the molecular geometry in D(1) ← S(2) and D(0) ← S(1).

Dissociation Potential Curves of Low-Lying States in Transition Metal Hydrides. 3. Hydrides of Groups 6 and 7

The dissociation curves of low-lying spin-mixed states in monohydrides of groups 6 and 7 were calculated by using an effective core potential (ECP) approach. This approach is based on the multiconfiguration self-consistent field (MCSCF) method, followed by first-order configuration interaction (FOCI) calculations, in which the method employs an ECP basis set proposed by Stevens and co-workers (SBKJC) augmented by a set of polarization functions. Spin-orbit coupling (SOC) effects are estimated within the one-electron approximation by using effective nuclear charges, since SOC splittings obtained with the full Breit-Pauli Hamitonian are underestimated when ECP basis sets are used. The ground states of group 6 hydrides have Omega = (1)/(2)(X(6)Sigma(+)(1/2)), where Omega is the z component of the total angular momentum quantum number. Although the ground states of group 7 hydrides have Omega = 0(+), their main adiabatic components are different; the ground state in MnH originates from the lowest (7)Sigma(+), while in TcH and ReH the main component of the ground state is the lowest (5)Sigma(+). The present paper reports a comprehensive set of theoretical results including the dissociation energies, equilibrium distances, electronic transition energies, harmonic frequencies, anharmonicities, and rotational constants for several low-lying spin-mixed states in these hydrides. Transition dipole moments were also computed among the spin-mixed states and large peak positions of electronic transitions are suggested theoretically for these hydrides. The periodic trends of physical properties of metal hydrides are discussed, based on the results reported in this and other recent studies.

Charge transfer to solvent (CTTS) energies of small X−(H2O)n=1–4 (X=F, Cl, Br, I) clusters: Ab initio study

Charge transfer to solvent (CTTS) energies of small halide–water clusters, X−(H2O)n=1–4 (X=F, Cl, Br, I) have been studied using first-order configuration interaction as well as time dependent discrete Fourier transform density functional methods. The only available experimental data are the recently reported CTTS energies for I−(H2O)n=1–4 clusters by Johnson and co-workers [D. Serxner, C. E. H. Dessent, and M. A. Johnson, J. Chem. Phys. 105, 7231 (1996)]. These results are in good agreement with our predicted values. The calculated CTTS energies indicate that there is regularity in the change of CTTS energies with respect to the change of halide anion as well as the cluster size. Our investigations have shown that this observed trend of CTTS energies of X−(H2O)n clusters could be quantitatively explained by the ionization potential of the halide anions and the binding energies of the respective clusters.

Effective Nuclear Charges for the First- through Third-Row Transition Metal Elements in Spin−Orbit Calculations

The effective nuclear charges (Zeff), which are empirical parameters in an approximate spin−orbit Hamiltonian, are determined for the first- through third-row transition metal elements by using experimental results for the fine structure splittings in atomic terms. All calculations use multiconfiguration self-consistent-field (MCSCF) wave functions, whose active space includes nd and (n + 1)sp orbitals (n is the principal quantum number), with the effective core potential (ECP) basis sets proposed by Stevens et al., augmented by one set of polarization f functions. First-order or second-order configuration interaction (FOCI or SOCI) calculations were also performed in order to understand disagreements between the MCSCF results and the experimental ones.

Spectroscopic properties and potential energy curves for 15 electronic states of palladium carbide (PdC)

Spectroscopic properties and potential energy curves of 15 electronic states of palladium carbide (PdC) have been obtained using the complete active-space multi-configuration self-consistent field (CAS-MCSCF) followed by first-order configuration interaction (FOCI) and multireference singles + doubles configuration interaction (MRSDCI) calculations that included 1.1 million configurations. The 1Σ + electronic state is found to be slightly lower than the 3Π state in the absence of spin–orbit coupling, but 3Π(0 +) becomes slightly lower with spin–orbit effects.

A theoretical study of the potential energy curves and spectroscopic constants of TaC and TaC +

Potential energy curves for the various low-lying electronic states of TaC and TaC + have been studied using the complete active space multiconfiguration self-consistent field method (CASMCSCF) followed by first-order and restricted second-order configuration (FOCI, SOCI) interaction calculations. The effect of spin–orbit interactions has been studied using the relativistic configuration interaction method. The ground state of TaC has been found to be 2Σ + whereas two nearly degenerate states ( 1Σ +, 3Σ +) are found as candidates for the ground state of TaC +. Inclusion of spin–orbit effect yields a state 1/2 as the ground state of TaC, while in case of TaC + 1 and 0 − states are very close in energy.

Electronic states and potential energy surfaces of rhodium carbide (RhC)

Potential energy curves and spectroscopic constants of 23 electronic states of the rhodium carbide (RhC) have been studied using the complete-active-space multi-configuration self-consistent field (CASMCSCF) followed by first-order configuration interaction (FOCI) calculations. Multi-reference singles + doubles configuration interaction (MRSDCI) were used to determine the properties of low-lying electronic states. The nature of chemical bond formation in different states is discussed in terms of their wave function and Mulliken populations.

Molecular quadrupole moment functions of HF and N2. I. Ab initio linear-response coupled-cluster results

The orthogonally spin-adapted linear-response coupled-cluster (LRCC) theory with singly and doubly excited clusters (CCSD) was employed to calculate quadrupole moment functions of the HF and N2 molecules in their ground electronic states. We also calculated several potential energy curves for both systems using various CC and non-CC methods, ranging from the limited and full configuration interaction (CI) and first-order CI (FOCI) to finite-order many-body perturbation theory. FOCI and related complete active space self-consistent field (CASSCF) methods were used in both energy and quadrupole moment calculations. Most of the calculations were performed using the medium-size basis set of TZ+2P quality devised by Sadlej [A. Sadlej, Coll. Czech. Chem. Commun. 53, 1995 (1988)] for high-level ab initio calculations of electrostatic molecular properties. In addition, a number of model CC calculations using small basis sets were performed, for which the exact full CI results, both for the energy and multipole moments, are available. It was demonstrated that the CCSD approach provides a realistic description of quadrupole moment functions, for all relevant geometries in the case of HF and for internuclear separations up to 1.5 times the equilibrium bond length for N2. The results of this study will be used for the analysis of the rovibrational dependence of quadrupole moments and for the calculation of quadrupole transition moments for both HF and N2.

Spectroscopic Properties of PtN

Spectroscopic properties of 21 electronic states of PtN are computed using complete active space multiconfiguration self-consistent field computations followed by first-order configuration interaction computations. Potential energy curves of several electronic states of PtN are reported. The multireference singles + doubles configuration interaction and the relativistic configuration interaction techniques are used to compare the properties of the low-lying states. Results of our computations agree not only with the known spectra of PtN but also predict several new electronic states which are yet to be observed.

The low-lying electronic states and harmonic vibrational frequencies of HCB, HBC, HCB − and HBC −

The low-lying singlet and triplet states of HCB and HBC, and doublet states of HCB − and HBC − are examined using ab initio molecular orbital theory at the HF/TZPP, FOCI/MCSCF level. For the neutral molecules, several new low-lying electronic states are found, and the linear triplet structures are found to have the lowest energy. For the anions, the 2 Σ + states are lower in energy than the 2 Π states. For HCB, the 3 Π state is 15.38 kcal mol −1 more stable than the 3 Σ − state, and for HBC the 3 Π is 2.51 kcal mol −1 below the 3 Σ − state at the first order configuration interaction (FOCI) level. The barriers to conversion of HBC( 3Π to HCB( 3Π) , HBC( 1Δ( 1 A 1)) to HCB( 1 A′C s) and HBC( 1 Δ( 1 A 2)) to HCB( 1A″ C s) are 23.21, 12.97 and 21.09 kcal mol −1, respectively. The activation energies to conversion of HBC − ( 2Σ +) to HCB − ( 2Σ +) and HCB − ( 2Π) to HBC − ( 2Π) are 18.13 and 25.88 kcal mol, respectively. The energies of fragmentation of HCB and HBC, and the harmonic vibrational frequencies of the neutral molecules and the anions are also reported to provide information for the possible experimental observation of these species.

Second-order perturbation theory using correlated orbitals. I. Full-valence reference functions

Abstract Recent developments of performant perturbation treatments on multiconfiguration wave functions have renewed interest in the coupling of variational and perturbative methods. In this communication it is shown that the choice of both the orbitals and the perturbation Hamiltonian to be used is as crucial as the choice of the reference space for obtaining accurate results. Moller-Plesset and Epstein-Nesbet perturbation series are applied to full-valence configuration interaction (FVCI) wave functions built on MCSCF (multi-configurational self-consistent field), FOCI (first-order configuration interaction) and SOCI (second-order configuration interaction) natural orbitals. Applications are presented for the following well-known systems: CH2 (X3B1−a1A1), CH2+ (X2A1, 1 2B1, 12A2, 1 2B2), SiH2 (X1A1, a 3B1, A 1B1) and NH2 (X 2A1, A 2B1). The results are compared to the corresponding full configuration interaction (FCI) when available.

The electronic excited states of the H-bonded complex of the phenol cation and water

Complete active space multireference first-order configuration interaction (FOCI) calculations are used to determine the excitation energies of organic radicals. Application is made to the analysis of the effect of H-bonded interactions on the spectra of the phenoxyl radical and the phenol cation. Although earlier tests have been successful, the FOCI excitation energies of the benzyl radical, which is isoelectronic with phenoxyl, is compared to both experiment and earlier multiconfiguration self-consistent field (MCSCF) values providing additional corroboration of the accuracy of FOCI methods. The well-known 398 nm transition in the pheoxyl radical is represented well by the FOCI calculation. Two additional lower energy transitions are also predicted. The transition at 461 nm in vacuo is assigned to a broad experimental fluorescence band observed in the 425 nm region. No spectrum of the phenol cation has been reported. A broad transition around 373 nm has been attributed to the phenol cation complex with a single water molecule. Shifts in. the spectra of the phenol cation and phenoxyl complexes relevant to the analysis of this transition are calculated to be of the order of 500cm −1. This result supports the spectral assignment to the phenol cation complex and the conclusion that proton transfer does not occur in the ground state of this complex.

Spectroscopic Properties and Potential Energy Curves for 21 Electronic States of CrH

Spectroscopic constants and potential energy curves of 21 electronic states of CrH are obtained using the all-electron complete active space multiconfiguration self-consistent field (CASMCSCF) followed by first-order configuration interaction (FOCI) and full second-order CI (SOCI) and multireference CI including Rydberg states calculations. The ground state of CrH is found to be of 6Σ+ symmetry with re = 1.690 Å, ωe = 1592 cm−1, De = 2.11 eV, and μe = 3.864 D at the SOCI level. Several optical transitions for CrH are predicted. Our computations support the reassignment of the state perturbing the A-X system to 4Σ+ suggested by Ram et al. Our computed spectroscopic constants for the A, X, and a 4Σ+ state are in excellent agreement with the experimental values reported by Ram et al.

Spectroscopic Constants and Potential Energy Curves of PbI

The spectroscopic constants and potential energy curves of the PbI diatomic were computed using complete active space SCF (CASSCF) followed by first-order CI (FOCI) and second-order CI (SOCI) calculations which included 607 000 configurations. Spin-orbit coupling was studied using the relativistic CI (RCI) method. The spectroscopic properties of the 2Π1/2 state are Re = 2.885 Å, ωe, = 153 cm−1, and De = 2.54(eV), while for the 2Π3/2 state the corresponding values are Re = 2.859 Å, ωe = 162 cm−1, and Te = 8255 cm−1. Our computed constants are in good agreement with experiment for the observed states. We also computed the properties and curves for several excited states which are yet to be observed.

Reaction field calculation of the spectral shifts of indole

Abstract : The excitation energy of indole has been investigated at geometries relevant to both the absorption and emission spectra using first-order configuration interaction (FOCI) methods. The calculation focused on the shift in the relative energy between the two excited states, L sub B and L sub A, and the excitation energies with geometry. A reaction field (RF) calculation also examined the shift in excitation energies when the molecule is dissolved in water. The excited states are found to be separated in vacuo by about 4,500 /cm at both the ground state and an approximation to the equilibrium L sub B geometry, M, and by 2,500/cm at the optimized geometry of both the first triplet excited state, T, and the first excited singlet state represented by a singles-only configuration interaction (S1). In water, the excited states are essentially degenerate and axed at the ground-state geometry. However, at the excited-states geometries, M and T, the L sub A state is shifted lower in energy than the L sub B state due to the large L sub A excited-state RF. At the S1 geometry, the electronic behavior of the two excited states is different from that at the other geometries. An approximation to the L sub A state is now the lower state both in vacuo and in the presence of the RF. There is a large calculated solvent fluorescent red shift in water at any geometry as well substantial Franck-Condon (FC) shift due to the steeper energy surface in the ground state compared to the excited states. The calculated energy shifts, dipole moments, and relative transition dipoles are in qualitative accord with experiment. However, the calculated fluorescent reaction dipoles are substantially larger than estimated in earlier studies. (jg)

Spectroscopic Properties and Potential Energy Curves for 30 Electronic States of ReH

Spectroscopic constants and potential energy curves of 30 electronic states of the diatomic ReH are computed using complete active space multiconfiguration self-consistent field followed by first-order configuration interaction (CI) and multireference singles + doubles CI calculations. The second-order CI calculations are made on four low-lying electronic states ( T e ≤ 10 000 cm −1). We also carry out relativistic Cl calculations including spin-orbit coupling to compute spin-orbit effects on the low-lying states of ReH. The ground state of ReH is found to be of 7Σ + symmetry ( R e = 1.82 Å, ω e = 1611 cm −1, D e = 1.3 eV) with a very low-lying excited state of 5Σ + symmetry ( T e ∼ 3000 cm −1) in the absence of spin-orbit effects. The analysis of the wavefunctions and Mulliken populations reveals that all the low-lying electronic states of ReH are very ionic (Re +H −). The Re atom has an effective configuration of 6 s 1.156 p 0.405 d 5.01 and 6 s 1.756 p 0.065 d 5.09 in the 7Σ + and 5Σ + states, respectively. The ReH σ bond in the 7Σ + ground state has 45% Re( s), 16% Re( p), and 39% Re( d) character while in the 5Σ + state, it has 60% Re( s), 2% Re( p), and 38% Re( d) character.

Theoretical investigation of the dissociation of bridged disilyne

The dissociation potential energy surfaces of ground-state bridged disilyne ( 1A 1), the Si 2H 2 global minimum, is investigated using the state-averaged multi-configuration self-consistent field (SA-MCSCF) method. The dissociation energy of bridged disilyne into Si 2 ( 1Δ g+H 2( 1Σ + g) is predicted to be 42 kcal/mol. The very small calculated energy barrier (about 1 kcal/mol) given by the SA-MCSCF calculations disappears at the first-order configuration interaction level of theory. The spin-orbit coupling constant between the lowest 1A 1 and 3B 1 states is estimated to be about 60 cm −1 in the crossing region of their potential energy surfaces.

Calculation of disulfide neutral and anion molecular excitation energies

The calculation of exited state of molecule require a multireference decription of the wave function. First-order configuration interaction (FOCI) calculations provide such a description but are still feasible for relatively large systems. A test of the method is provided by modeling the spectra of the S-S - bond with the molecules HSS - and CH 3 SS - . The first excitation energy is assigned to a band in the rhodanese enzyme that has been attributed to a S-S - bond at the enzyme active site. The broad absorption spectra of the corresponding neutral molecules can also be understood from the FOCI calculations

Spectroscopic constants and potential energy curves for 18 electronic states of IrH +

Spectroscopic constants and potential energy curves of 18 electronic states of IrH + are obtained using the complete active space multi-configuration self-consistent field (CASMCSCF) followed by first-order configuration interaction (FOCI) and multi-reference singles + doubles CI (MRSDCI) calculations. The spin-orbit effects are introduced using the relativistic-configuration-interaction (RCI) method. The ground state of IrH + is found to be of 4Σ − symmetry with r e = 1.548 A ̊ , ω e = 2296 cm −1, and D e = 3.28 eV in the absence of spin-orbit interactions, while three nearly degenerate states [ 1 2 ( I) , 1 2 ( II) , 9 2 ( I) ] are found as candidates for the ground state including spin-orbit coupling. Several optical transitions for IrH + are predicted, none of which has been observed experimentally. The nature and bonding of the low-lying electronic states are analyzed.