Multireference Configuration Interaction Wave Functions Research Articles

Analysis of and remedies for unphysical ground states of the multireference averaged coupled-pair functional

A Multireference Configuration Interaction (MRCI) wavefunction includes both static and dynamic electron correlation. MRCI's well-known flaw, a lack of size extensivity, can be ameliorated with the Multireference Averaged Coupled-Pair Functional (MRACPF). However, the original MRACPF is frequently unstable, sometimes producing unphysical results. The more Multireference Averaged Quadratic Coupled-Cluster and MRACPF2 functionals also occasionally exhibit unphysical behavior. We find that these instabilities are avoided crossings with unphysical solutions to the MRACPF equations. We present two approaches to avoid the undesirable unphysical solutions.

Ultrafast non-adiabatic dynamics of ethylene including Rydberg states

The photodynamics of ethylene has been studied by means of ab initio surface-hopping dynamics using extended multireference configuration interaction wavefunctions. At the highest level, the explicit possibility of excited-state CH dissociation and consideration of the Rydberg π−3s state was included into the electronic wavefunction. The initial dynamics is characterised by the torsional motion and the crossing between the bright π−π * state with S 1, the latter having primarily Rydberg character with only a minor contribution of the repulsive valence π−σ * state. Due to back-rotation to planar structures after 17 fs, part of the population flows into the Rydberg states. The lifetime for this fraction of trajectories is significantly longer than that for the valence population. An analysis of the latter population shows that the decay to the ground state proceeds mainly at the pyramidalised conical intersection. Thus, no major qualitative mechanistic changes as compared to previous dynamics simulations are observed for the valence population. In the present work, a decay time of 62 fs was found for the valence population. Simulations performed for ethylene-d4 show a slowdown of the torsional mode. However, since the crossing seam is reached in a more direct way with less torsional oscillations, the excited-state lifetime is almost unchanged as compared to ethylene.

On the mechanism for the nonadiabatic reactive quenching of OH(A2Σ+) by H2(1$\Sigma _{\rm g}^+$Σg+): The role of the 22A state

A scheme for reactive electronic quenching of OH(A(2)Σ(+)) through collisions with H2 is proposed, supported by electronic structure data obtained from multireference configuration interaction wave functions. The scheme represents an insertion pathway that leads from the initial 3(2)A state in the reactant channel, into a valence region, where a nonadiabatic transition to the 2(2)A state, enabled by a 2(2)A-3(2)A conical intersection seam occurs. Once on the 2(2)A state, insertion of HO into H2 provides access to a linking region and, after surmounting a small barrier, to a region where the low-lying electronic states are Rydberg in character, corresponding to the 3s, 3p(x), 3p(y), and 3p(z) states of OH3(+). In the Rydberg region, a deep well on the 2(2)A potential energy surface exists. Direct passage from the 2(2)A state to ground state products, H2O(X(1)A1) + H, is precluded by an energy barrier so that an intermediate complex can be formed on the 2(2)A potential energy surface. As the insertion is facilitated by rehybridization of the oxygen orbitals from sp to sp(3) in the linking region, nonplanar approach of HO to H2 is favored. The precipitous change in electronic structure from valence to Rydberg character renders the linking region inaccessible on the 3(2)A potential energy surface. From the 2(2)A state in the Rydberg region, access to the H2O + H product channel is enabled by repeated passage through a region of appreciable 1(2)A-2(2)A derivative coupling or by radiative decay. This scheme supplements other pathways in which nonadiabatic transitions from the 2(2)A state to the 1(2)A state in the valence region enable both planar and nonplanar insertion and abstraction paths leading directly to H2O products.

Unusual Inorganic Biradicals: A Theoretical Analysis

The biradical character β (1 for an ideal biradical) is determined from multi-reference configuration interaction (MRCI) wavefunctions. Triatomics in the series FX2+ (X=O, S, Se, Te, Po) exhibit unusually high biradical characters for X=Te, Po (0.76<β<0.92), the largest among the homologous 18 valence electron molecules CX22−, NX2−, X3, and OX2. On the same scale, the biradical character of O3 is just 0.19, whereas that of C(CH2)3 is 0.97.

Multi-reference configuration-interaction calculations on multiply charged ions of carbon monosulfide

The potential energy curves for neutrals and multiply charged ions of carbon monosulfide are computed with highly correlated multi-reference configuration interaction wavefunctions. The correlations of inner-shell electrons with the scalar relativistic effects are included in the present computations. The spectroscopic constants, dissociation energies, ionization energies for ground and low-lying excited states together with corresponding electronic configurations of ions are obtained, and a good agreement between the present work and existing experiments is found. No theoretical evidence is found for the adiabatically stable CSq+ (q > 2) ions according to the present ab initio calculations. The calculated values for 1st–6th ionization energies are 11.25, 32.66, 64.82,106.25,159.75, and 224.64 eV, respectively. The kinetic energy release data of fragments are provided by the present work for further experimental comparisons.

Investigation on the potential energy curves and spectroscopic properties of the low-lying excited states of BP

The multi-reference configuration interaction (MRCI) method in quantum chemistry is used to investigate the BP+ at the level of aug-cc-pVQZ basis set. The potential energy curves of 6 Λ-S states of BP+ radical are obtained, which can be correlated to the dissociation limit B+(1Sg)+P(4Su), B+(1Sg)+P(2Du) and B+(1Sg)+P(2Pu). In order to get the accurate potential energy curves, the Davidson correction (+Q) and scalar relativistic effect are taken into consideration. Analyses of the electronic structures of Λ-S states demonstrate that the Λ-S electronic states are multi-configurational in nature. The spin-orbit interaction is considered for the first time sofar as we have, which makes 6 Λ-S states split to 10 Ω states. The calculation results show that the crossing between the Ω states of the same symmetry can be aveided. Then the spectroscopic constants of the bound Λ-S and Ω states are obtained by solving the radial Schrödinger equation with the program LEVEL8.0 according to the MRCI wave functions. By comparing with available experimental results, the spectroscopic constants of ground states are in good agreement with the available theoretical values. The remaining computational results in this paper are reported also for the first time.

Time-dependent Wave Packet Quantum Scattering Study of Reaction S(3P)+H2→HS+H on a Newab initioPotential Energy Surface 3A′

A new potential energy surface is presented for the triplet state 3A′ of the chemical reaction S(3P)+H2 from a set of accurate ab initio data. The single point energies are computed using highly correlated complete active space self-consistent-field and multi-reference configuration interaction wave functions with a basis set of aug-cc-pV5Z. We have fitted the full set of energy values using many-body expansion method with an Aguado-Paniagua function. Based on the new potential energy surface, we carry out the time-dependent wave packet scattering calculations over the collision energy range of 0.8-2.2 eV. Both the centrifugal-sudden approximation and Coriolis Coupling cross sections are obtained. In addition, the total reaction probabilities are calculated for the reactant H2 initially in the vibrational states v=0–3 (j=0). It is found that initial vibrational excitation enhances the title reaction.

New ab initio coupled potential energy surfaces for the Br(2P3/2, 2P1/2) + H2 reaction

The three lowest (1A('), 2A('), and 1A('')) adiabatic potential energy surfaces (PESs) for the Br((2)P) + H(2) reactive system have been computed based on the multi-reference configuration interaction (MRCI) method including the Davidson's correction with a large basis set. These three adiabatic PESs have been transformed to a diabatic representation, leading to four coupling potentials. In addition, the spin-orbit matrix elements were also obtained using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Consequently, six coupling potentials were obtained and their characteristics were extensively discussed. Nonadiabatic quantum dynamics calculations for this system have been realized with these realistic diabatic potentials instead of previous semi-empirical diabatic potentials. Based on two-state model nonadiabatic calculations for the Br((2)P(3∕2), (2)P(1∕2)) + H(2) reaction, the Br((2)P(1∕2)) + H(2) reaction was found to show less reactivity than the Br((2)P(3∕2)) + H(2) reaction at collision energies beyond the threshold of the Br((2)P(3∕2)) + H(2) reaction. Our results are consistent with the previous studies on the XH(2) (X = F, Cl) system, which indicate that the adiabatically forbidden channel is dominant at low energies in the open-shell halogen atom plus H(2) reactions.

New ab initio potential energy surface for BrH2 and rate constants for the H + HBr → H2 + Br abstraction reaction

A global potential energy surface (PES) for the electronic ground state of the BrH(2) system was constructed based on the multireference configuration interaction (MRCI) method including the Davidson's correction using a large basis set. In addition, the spin-orbit correction were computed using the Breit-Pauli Hamiltonian and the unperturbed MRCI wavefunctions in the Br + H(2) channel and the transition state region. Adding the correction to the ground state potential, the lowest spin-orbit correlated adiabatic potential was obtained. The characters of the new potential are discussed. Accurate initial state specified rate constants for the H + HBr → H(2) + Br abstraction reaction were calculated using a time-dependent wave packet method. The predicted rate constants were found to be in excellent agreement with the available experimental values and much better than those obtained from a previous PES.

Theoretical study of collision and collision-free radiative lifetimes of $ {{\text{S}}_2}\left( {{{\text{B}}^3}\Sigma_{\text{u}}^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) $

We calculate multireference configuration-interaction wavefunctions and the potential-energy curves for the \( {B^3}\Sigma_u^{-} \) and \( {X^3}\Sigma_g^{-} \) states of the collision-free S2 molecule and the T-shape collision complex S2–He using cc-pVQZ basis sets. We obtain the transition dipole moments of the \( {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \to {X^3}\Sigma_g^{-} } \right) \) and the Franck–Condon factors between the vibrational levels of this two states. We evaluate the radiative lifetimes of \( {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) \) levels of the collision complex and the collision-free molecule and compare them with the experiments. The collision provides little change in the radiative lifetimes of \( {{\text{S}}_2}\left( {{B^3}\Sigma_u^{-} \left( {{\upsilon^{\prime}} = 0 - 9} \right)} \right) \) according to the previous calculations. We obtain excellent agreement between the theoretical results and the experiments. The data calculated are very useful in the study of the microwave-driven high-pressure sulfur lamp and an S2 laser pumped by a transverse fast discharge.

Relativistic multireference many-body perturbation theory for open-shell ions with multiple valence shell electrons: the transition rates and lifetimes of the excited levels in chlorinelike Fe X

A recently developed relativistic multireference many-body perturbation theory based on multireference configuration-interaction wavefunctions as zeroth-order wavefunctions is outlined. The perturbation theory employs a general class of configuration-interaction wavefunctions as reference functions, and thus is applicable to multiple open valence shell systems with near degeneracy of a manifold of strongly interacting configurations. Multireference many-body perturbation calculations are reported for the ground and excited states of chlorinelike Fe X in which the near degeneracy of a manifold of strongly interacting configurations mandates a multireference treatment. Term energies of a total of 83 excited levels arising from the 3s23p5, 3s3p6, 3s23p43d, 3s3p53d, and 3s23p33d2 configurations of the ion are evaluated to high accuracy. Transition rates associated with E1/M1/E2/M2/E3 radiative decays and lifetimes of a number of excited levels are calculated and compared with laboratory measurements to critically evaluate recent experiments.

Exact quantum scattering study of the Ne+H2+ reaction on a new ab initio potential energy surface

We present a new potential energy surface (PES) for the ground state (1(2)A(')) of the chemical reaction Ne+H(2) (+) from a set of accurate ab initio data, which were computed using highly correlated complete active space self-consistent field and multireference configuration interaction wave functions with a basis set of aug-cc-pV5Z. The quantum reactive scattering dynamics calculation was carried out over the collision energy (E(col)) range of 0.5-1.5 eV based on the new PES. In this work we have taken the Coriolis coupling (CC) effect into account. The importance of including the CC quantum scattering calculation has been revealed by the comparison between the CC and the centrifugal sudden approximation calculation. The magnitude and profile of the CC total cross sections for v=0 and j=1 over the collision energy range of 0.5-1.5 eV are found to be in good agreement with the available experimental measurements obtained recently by Zhang et al. [J. Chem. Phys. 119, 10175 (2003)] after taking into account the experimental uncertainties.

Structures and Energetics of H6+ Clusters

Theoretical investigations of the equilibrium structures and associated isomerization reactions of the hydrogen clusters H(6)(+) have been carried out. Three equilibrium structures and three isomerization transition states were located on the electronic doublet and quartet states of the respective potential energy surfaces. The research employed ab initio self-consistent-field (SCF), coupled cluster (CC) with single and double excitations (CCSD), CCSD with perturbative triple excitations (CCSD(T)), and full triple excitations (CCSDT) wave functions and a wide variety of correlation-consistent polarized valence cc-pVXZ and aug-cc-pVXZ (where X = D, T, Q) basis sets. For each structure the geometry, energy, dipole moment, harmonic vibrational frequencies, and infrared intensities are predicted. Complete active space SCF (CASSCF) and multireference configuration interaction (MRCI) wave functions are used to analyze the effect of correlation on physical properties and energetics. Extensive focal point analyses (including CCSDTQ and full CI energies and basis sets up to sextuple zeta) are used to obtain complete basis set (CBS) limit energies. The H(2)(+)-core H(6)(+) cluster with D(2d) symmetry is the global minimum, lying 3.9 (4.2) +/- 0.1 kcal mol(-1) below the H(3)(+)-core H(6)(+) cluster with C(s) symmetry, where zero-point vibrational energy (ZPVE) corrected value are shown in parentheses. The barrier of the isomerization reaction between these two structures is 7.4 (5.2) +/- 0.1 kcal mol(-1). The dissociation energies for the H(2)(+)-core H(6)(+) isomer [H(6)(+) (D(2d)) --> 2H(2) + H(2)(+)] and the H(3)(+)-core H(6)(+) isomer [H(6)(+) (C(s)) --> H(3)(+) + H(2) + H] are 57.5 (50.9) +/- 0.1 and 12.3 (8.3) +/- 0.1 kcal mol(-1), respectively.

The Photoelectron Spectrum of Pyrrolide: Nonadiabatic Effects due to Conical Intersections

The negative ion photoelectron spectrum of the pyrrolide-h4 anion and the completely deuterated analogue, pyrrolide-d4, are computed employing the multimode vibronic coupling approach, based on a two-state, fully quadratic, quasi-diabatic Hamiltonian, Hd, which accurately represents the vicinity of the ab initio determined equilibrium geometry of the ground 2A2 state as well as the minimum energy crossing point (MECP) on the symmetry-allowed 2A2−2B1 accidental seam of conical intersection. The ab initio data are obtained from multireference configuration interaction wave functions based on triple-ζ quality atomic orbital bases. The determined photoelectron spectra, which are converged with respect to the vibronic basis, compare favorably with previous spectroscopic results, for pyrrolide-h4. The principal impact of the seam of conical intersection is a significant perturbation of the portion of the spectrum attributable to the 2B1 state, in agreement with previous analyses. However, despite the fact that the MECP is approximately 0.5 eV above the 2A2 minimum, its manifestations are shown to be evident in the photoelectron spectrum near threshold. By comparing the simulated and measured photoelectron spectrum, it is deduced that the electronic transition moment for the production of the 2A2 state of pyrrolyl from pyrrolide is approximately twice that for the production of the 2B1 state.

Multireference (MR) configuration interaction (CI) approach for quasidegenerate systems

The multireference (MR) configuration interaction (CI) wavefunctions utilizing generalized Hartree-Fock (GHF) molecular orbitals are discussed in relation to our previous extended HF and recent full-valence MCSCF methods for quasidegenerate systems. The reaction natural orbitals (RNO) for constructing the reference functions are selected on the basis of GHF calculations. The computational procedures for the MR CI are illustrated by considering imino nitroxide (HNNO) as an example. It is found that the present MR CI provides well-balanced wavefunctions between the ground and lower-lying excited states of the species. The correlation corrections coming from higher-order excitations are examined by a Davidson-like formula. The relation of this formula to the coupled-cluster method is stressed.

Theoretical study of electric moments, polarizabilities, and fine and hyperfine coupling constants of the B3Πg, C3Πu, A′5Σg+, and C″5Πu states of N2This article is part of a Special Issue on Spectroscopy at the University of New Brunswick in honour of Colan Linton and Ron Lees.This paper is dedicated to Professors Ronald M. Lees and Colan Linton from the Department of

Several properties are calculated for the first time for the B3Πg, C3Πu, A′5Σg+, and C″5Πu states of N2, i.e., quadrupole (Θ) and hexadecapole (Φ) moments, static dipole polarizability (α), and hyperfine structure (hfs) data such as the electric field gradient (qii) and magnetic Frosch–Foley parameters (b, c, d). These quantities are evaluated with the density functional theory (DFT) method B3LYP/aug-cc-pVQZ. The variation with geometry is also considered for all parameters above. The B(σgπg) and C(σuπg) triplet Π states have similar values of the anisotropy P|2|(2) ∝ (Pxx − Pyy), with P = Θii, qii, or Tii (dipolar hfs tensor). The first-order spin-orbit coupling constant AΛ and the second-order electron-spin g-shift Δg⊥ are obtained with a 6-311+G(2d) basis and multireference configuration interaction (MRDCI) wave functions. Values of AΛ calculated for W3Δu and (B, C, C′, C″) Π states reproduce well the experimental data (C and C′ are two different minima of 13Πu). The variation of AΛ with R(N-N) is regular for all states studied, except for AΠ(13Πu), which changes abruptly between the C and C′ minima (from 38 to 2 cm−1). The Δg⊥ values — evaluated via sum over states expansions — are calculated for A′5Σg+ as well as A3Σu+ and B′3Σu−. The spin-rotation constant γΣ is derived via Curl’s equation γΣ = (−2B)Δg⊥. We find γΣ(A′) to be negative and to decrease steadily with vibrational excitation, in line with experimental observations. Both Δg⊥ and γΣ of A′5Σg+ are determined by the coupling of this weakly bound state with the strongly repulsive 15Πg state.

Determining quasidiabatic coupled electronic state Hamiltonians using derivative couplings: A normal equations based method

A self-consistent procedure for constructing a quasidiabatic Hamiltonian representing N(state) coupled electronic states in the vicinity of an arbitrary point in nuclear coordinate space is described. The matrix elements of the Hamiltonian are polynomials of arbitrary order. Employing a crude adiabatic basis, the coefficients of the linear terms are determined exactly using analytic gradient techniques. The remaining polynomial coefficients are determined from the normal form of a system of pseudolinear equations, which uses energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. In a previous implementation energy gradient and derivative coupling information were employed to limit the number of nuclear configurations at which ab initio data were required to determine the unknown coefficients. Conversely, the key aspect of the current approach is the use of ab initio data over an extended range of nuclear configurations. The normal form of the system of pseudolinear equations is introduced here to obtain a least-squares fit to what would have been an (intractable) overcomplete set of data in the previous approach. This method provides a quasidiabatic representation that minimizes the residual derivative coupling in a least-squares sense, a means to extend the domain of accuracy of the diabatic Hamiltonian or refine its accuracy within a given domain, and a way to impose point group symmetry and hermiticity. These attributes are illustrated using the 1 (2)A(1) and 1 (2)E states of the 1-propynyl radical, CH(3)CC.

Electronic states of BP, BP +, BP −, B 2P 2, [formula omitted] and [formula omitted

Using augmented sextuple zeta basis sets and internally contracted multireference configuration interaction (MRCI) wavefunctions, potential energy, electric dipole and transition moments have been computed for the X 3Π, a 1Σ +, b 1Π and A 3Σ − states of BP, X 2Σ + and A 2Π states of BP − and X 4Σ − and A 4Π states of BP +. From these data spectroscopic constants, radiative transition probabilities and photoelectron spectra of BP − and BP have been evaluated. The non-vanishing spin–orbit coupling elements between the four low lying triplet and singlet states of the neutral BP have also been calculated from MRCI wavefunctions. The treatment of the corresponding perturbations in the manifold of dense rovibrational states in the three lowest states would require a precise knowledge of the electronic excitation energies. Our best singlet–triplet separations (X–a) are calculated to be 2412 cm −1 (MRCI) and 2482 cm −1 (restricted coupled cluster with perturbative triples (RCCSD(T))) with an estimated error bound of about ±200 cm −1. All three states have long radiative lifetimes with cascading among the rovibrational levels of different states. The ionization energy IE e of BP is calculated to be 9.22 eV (MRCI) and 9.48 eV (RCCSD(T)), the electron affinity EA e 2.51 eV (MRCI) and 2.74 eV (RCCSD(T)). The photoelectron spectra of BP and BP − have been obtained from the Franck–Condon factors of the MRCI potentials. For the UV spectroscopy the dipole allowed radiative transition probabilities are given for A 3Σ − ↔ X 3Π, b 1Π ↔ a 1Σ + of BP, A 2Π ↔ X 2Σ + of BP − and A 4Π ↔ X 4Σ − of BP +. The ionization energy IE e of B 2P 2 of 8.71 eV and the electron affinity EA e of 2.34 eV have been calculated by the RCCSD(T)/aVQZ approach. Also the harmonic vibrational wavenumbers for the electronic ground states of the ions B 2 P 2 + and B 2 P 2 - are given.

Analytic derivative calculation of electronic g-tensors based on multireference configuration interaction wavefunctions

A computer program has been written to perform analytic derivative calculations of magnetic response properties based on uncontracted multireference configuration interaction (MRCI) wavefunctions. At this point, orbital relaxation is neglected in this treatment and the basis functions are assumed to be independent of the perturbation. It is therefore equivalent to an untruncated sum-over-states (SOS) approach to the g-tensor. Hence, the treatment is more rigorous than all previous MRCI g-tensor calculations that have used truncated SOS formulations. In the present calculations, MRCI calculations were performed on top of full valence complete-active space self-consistent field (CASSCF) reference wavefunctions without truncation of the reference or correlation spaces. Results are reported for two types of spin–orbit coupling operators, a simple effective nuclear charge approximation and the spin–orbit mean field (SOMF) approximation. The effects of orbital relaxation are discussed. The values obtained can be used in future calibration studies.

On the vibronic coupling approximation: A generally applicable approach for determining fully quadratic quasidiabatic coupled electronic state Hamiltonians

In this report we introduce an iterative procedure for constructing a quasidiabatic Hamiltonian representing N(state)-coupled electronic states in the vicinity of an arbitrary point in N(int)-dimensional nuclear coordinate space. The Hamiltonian, which is designed to compute vibronic spectra employing the multimode vibronic coupling approximation, includes all linear terms which are determined exactly using analytic gradient techniques. In addition, all [N(state)][N(int)] quadratic terms, where [n]=n(n+1)/2, are determined from energy gradient and derivative coupling information obtained from reliable multireference configuration interaction wave functions. The use of energy gradient and derivative coupling information enables the large number of second order parameters to be determined employing ab initio data computed at a limited number of points (N(int) being minimal) and assures a maximal degree of quasidiabaticity. Numerical examples are given in which quasidiabatic Hamiltonians centered around three points on the C(3)H(3)N(2) potential energy surface (the minimum energy point on the ground state surface and the minimum energy points on the two- and three-state seams of conical intersection) were computed and compared. A method to modify the conical intersection based Hamiltonians to better describe the region of the ground state minimum is introduced, yielding improved agreement with ab initio results, particularly in the case of the Hamiltonian defined at the two-state minimum energy crossing.