Variational Configuration Interaction Research Articles

Exact-Two-Component Relativistic Multireference Second-Order Perturbation Theory.

As the relativistic corrections become stronger for late-row elements, the fully perturbative treatment of spin-orbit coupling and dynamic correlation may become inadequate for accurate descriptions of chemical properties. In this work, we introduce a determinant-based Kramers-unrestricted exact-two-component multireference second-order perturbation (X2C-MRPT2) method which variationally includes relativistic corrections with a perturbative dynamic correlation. The restricted active space partitioning scheme is employed to provide an adjustable correlation space for the second-order perturbation treatment. The multistate perturbation theory is also developed to improve the descriptions of ground and excited states. Benchmark studies of atomic fine-structure splittings and spectroscopic constants of molecular monohydrides using X2C-MRPT2 are compared to the other perturbative and variational approaches. The results suggest that X2C-MRPT2 is a highly accurate alternative to the fully variational multireference configuration interaction method at only a small fraction of the computational cost.

Efficient and automated quantum chemical calculation of rovibrational nonresonant Raman spectra.

An outline of a newly developed program for the simulation of rovibrational nonresonant Raman spectra is presented. This program is an extension of our recently developed code for rovibrational infrared spectra [Erfort et al., J. Chem Phys. 152, 244104 (2020)] and relies on vibrational wavefunctions from variational configuration interaction theory to allow for an almost fully automated calculation of such spectra in a pure ab initio fashion. Due to efficient contraction schemes, this program requires modest computational resources, and it can be controlled by only a few lines of input. As the required polarizability surfaces are also computed in an automated fashion, this implementation enables the routine application to small molecules. For demonstrating its capabilities, benchmark calculations for water H2 16O are compared to reference data, and spectra for the beryllium dihydride dimer, Be2H4 (D2h), are predicted. The inversion symmetry of the D2h systems lead to complementary infrared and Raman spectra, which are both needed for a comprehensive investigation of this system.

Parity-violation effects in the vibrational spectra of CHFClBr and CDFClBr

Relativistic four-component electronic structure calculations at the density functional level have been carried out to describe parity-violation (PV) energy shifts to the total electronic energy for the chiral molecule CHFClBr. An $n$-mode ($n=3,4$) expansion of the complete potential energy surface at the explicitly correlated coupled-cluster level has been used for the vibrational analysis of PV effects for CHFClBr and CDFClBr. The vibrational spectrum and corresponding absolute intensities for fundamental, overtone, and combination band transitions obtained from a variational configuration interaction treatment are in excellent agreement with experimental data and the most accurate so far obtained. The results show that a 3-mode expansion is sufficient for the vibrational analysis. The PV energy shifts for the fundamental, overtone, and combination bands are all in the mHz region. The data provided will be useful for future detection of PV in chiral molecules.

Characterizing structures, energetics, and spectra of species on the 1,3[H, C, As] potential energy surfaces: A high-level theoretical contribution.

The ground and the low lying electronic states of structures on the 1,3[H, C, As] potential energy surfaces were investigated with the highly correlated theoretical approaches CCSD(T), CCSD(T)-F12b, and CASSCF/MRCI along with the series of correlation consistent (aug-cc-pVnZ, n = D, T, Q, 5) basis sets. Energetic and spectroscopic parameters were obtained at the complete basis set limit, and the effect of core-valence correlation on these properties evaluated. Fundamental frequencies were also computed with the variational configuration interaction (VCI) approach. Heats of formation at 0 and 298.15 K were estimated for HCAs and CH, AsH, CAs, and HCAs, as well as the calculation of ionization potentials for HCAs. Comparisons of the present results with literature ones for the systems HCN/HNC, HCP/HPC highlight similarities and differences among these systems. Altogether, this investigation provides a very reliable characterization of the species on the surfaces and should guide future experimental studies on these systems.

Crystal Field Splittings in Lanthanide Complexes: Inclusion of Correlation Effects beyond Second Order Perturbation Theory.

State-averaged complete active space self-consistent field (CASSCF) calculations and a subsequent spin-orbit calculation mixing the CASSCF wave functions (CASSCF/state-interaction with spin-orbit coupling) is the conventional approach used for ab initio calculations of crystal-field splittings and magnetic properties of lanthanide complexes. However, this approach neglects dynamical correlation. Complete active space second-order perturbation theory (CASPT2) can be used to account for dynamical correlation but suffers from the well-known problems of multireference perturbation theory, e.g., intruder state problems. Variational multireference configuration interaction (MRCI) calculations do not show these problems but are usually not feasible due to the large size of real lanthanide complexes. Here, we present a quasi-local projected internally contracted MRCI approach which makes MRCI calculations of lanthanide complexes feasible and allows assessing the influence of dynamical correlation beyond second-order perturbation theory. We apply the method to two well-studied molecules, namely, [Er{N(SiMe3)2}3] and {C(NH2)3}5[Er(CO3)4]·11H2O.

Multi-reference vibration correlation methods

State-specific vibration correlation methods beyond the vibrational multi-configuration self-consistent field (VMCSCF) approximation have been developed, which allow for the accurate calculation of state energies for systems suffering from strong anharmonic resonances. Both variational multi-reference configuration interaction approaches and an implementation of approximate 2nd order vibrational multi-reference perturbation theory are presented. The variational approach can be significantly accelerated by a configuration selection scheme, which leads to negligible deviations in the final results. Relaxation effects due to the partitioning of the correlation space and the performance of a VMCSCF modal basis in contrast to a standard modal basis obtained from vibrational self-consistent field theory have been investigated in detail. Benchmark calculations based on high-level potentials are provided for the propargyl cation and cis-diazene.

Symmetry breaking in a nutshell: The odyssey of a pseudo problem in molecular physics. The $\tilde X\,{}^2\Sigma _u^ + $X̃Σu+2 BNB case revisited

The X̃(2)Σu (+) BNB state considered to be of symmetry broken (SB) character has been studied by high level multireference variational and full configuration interaction methods. We discuss in great detail the roots of the so-called SB problem and we offer an in depth analysis of the unsuspected reasons behind the double minimum topology found in practically all previous theoretical investigations. We argue that the true reason of failure to recover a D∞h equilibrium geometry lies in the lack of the correct permutational symmetry of the wavefunctions employed and is by no means a real effect.

First principles exploration of NiO and its ions NiO+ and NiO−

We present a high level ab initio study of NiO and its ions, NiO(+) and NiO(-). Employing variational multireference configuration interaction (MRCI) and single reference coupled-cluster methods combined with basis sets of quintuple quality, 54, 20, and 10 bound states of NiO, NiO(+), and NiO(-) have been studied. For all these states, complete potential energy curves have been constructed at the MRCI level of theory; in addition, for the ground states of the three species core subvalence (3s(2)3p(6)∕(Ni)) and scalar relativistic effects have been taken into account. We report energetics, spectroscopic parameters, dipole moments, and spin-orbit coupling constants. The agreement with experiment is in the case of NiO good, but certain discrepancies that need further investigation have arisen in the case of the anion whose ground state remains computationally a tantalizing matter. The cation is experimentally almost entirely unexplored, therefore, the study of many states shall prove valuable to further investigators. The ground state symmetry, bond distances, and binding energies of NiO and NiO(+) are (existing experimental values in parenthesis), X(3)Σ(-)(X(3)Σ(-)), r(e) = 1.606 (1.62712) Å, D(0) = 88.5 (89.2 ± 0.7) kcal/mol, and X(4)Σ(-)(?), r(e) = 1.60(?) Å, D(0) = 55 (62.4 ± 2.4) kcal/mol, respectively. The ground state of NiO(-) is (4)Σ(-) (but (2)Π experimentally) with D(0) = 85-87 (89.2 ± 0.7) kcal/mol.

Vibrational frequencies and spectroscopic constants from quartic force fields for cis-HOCO: The radical and the anion

The use of accurate quartic force fields together with vibrational configuration interaction recently predicted gas phase fundamental vibrational frequencies of the trans-HOCO radical to within 4 cm(-1) of experimental results for the two highest frequency modes. Utilizing the same approach, we are providing a full list of fundamental vibrational frequencies and spectroscopic constants for the cis-HOCO system in both radical and anionic forms. Our predicted geometrical parameters of the cis-HOCO radical match experiment and previous computation to better than 1% deviation, and previous theoretical work agrees equally well for the anion. Correspondence between vibrational perturbation theory and variational vibrational configuration interaction for prediction of the frequencies of each mode is strong, better than 5 cm(-1), except for the torsional motion, similar to what has been previously identified in the trans-HOCO radical. Among other considerations, our results are immediately applicable to dissociative photodetachment experiments which initially draw on the cis-HOCO anion since it is the most stable conformer of the anion and is used to gain insight into the portion of the OH + CO potential surface where the HOCO radical is believed to form, and we are also providing highly accurate electron binding energies relevant to these experiments.

A linked electron pair functional

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an approximation to variational coupled cluster is generated through truncation of the exponential cluster operator. When combined, these methods demonstrate accuracy that exceeds that of the standard coupled-cluster method, in particular in situations where the reference Slater determinant is not a good approximation.

A theoretical approach to the photochemical activation of matrix isolated aluminum atoms and their reaction with methane

The photochemical activation of Al atoms in cryogenic matrices to induce their reaction with methane has been experimentally studied before. Here, a theoretical study of the nonadiabatic transition probabilities for the ground ((2)P:3s(2)3p(1)) and the lowest excited states ((2)S:3s(2)4s(1) and (2)D:3s(2)3d(1)) of an aluminum atom interacting with a methane molecule (CH(4)) was carried out through ab initio Hartree-Fock self-consistent field calculations. This was followed by a multiconfigurational study of the correlation energy obtained by extensive variational and perturbational configuration interaction analyses using the CIPSI program. The (2)D state is readily inserted into a C-H bond, this being a prelude to a sequence of avoided crossings with the initially repulsive (to CH(4)) lower lying states (2)P and (2)S. We then use a direct extension of the Landau-Zener theory to obtain transition probabilities at each avoided crossing, allowing the formation of an HAlCH(3) intermediate that eventually leads to the final pair of products H+AlCH(3) and HAl+CH(3).

Shape of the geometrically active atomic states of carbon

We have developed a computer code for ab initio the variational configuration interaction calculation of the electronic structure of atoms via variationally optimized Lagurre type orbitals, treating the orbital effective charges as variational parameters. Excited states of the same symmetry, in order to avoid the inherent restrictions of the standard method of Hylleraas–Unheim and MacDonald, are computed variationally by minimizing the recently developed minimization functionals for excited states. By computing, at the minimum, the one-electron density and the probability distribution of the two-electron angle, and the most probable two-electron angle, we investigate the atomic states of the carbon atom. We show that, without resorting to the (admittedly unproven) concept of hybridization, as an intrinsic property of the atomic wave function, the most probable value of the two-electron angle is around the known angles of carbon bonding, i.e. either 109° or 120° or 180°, depending on each low-lying state of the bare carbon atom.

Pair-vibrational states in the presence of neutron–proton pairing

Pair vibrations are studied for a Hamiltonian with neutron–neutron, proton–proton and neutron–proton pairing. The spectrum is found to be rich in strongly correlated, low-lying excited states. Changing the ratio of diagonal to off-diagonal pairing matrix elements is found to have a large impact on the excited-state spectrum. The variational configuration interaction (VCI) method, used to calculate the excitation spectrum, is found to be in very good agreement with exact solutions for systems with large degeneracies having equal T=0 and T=1 pairing strengths.

Calculation of geometrically active atomic state

We develop a computer code to calculate ab-initio variational configuration interaction of electronic structure of atoms via generalised Lagurre type orbitals. Treating the orbital effective charges as variational parameters and computing the absolute minimum of energy, yield its optimal wave function.Then utilizing the one-electron density and the probability distribution of the angular two-electron density according to the optimal wave function, we investigate the geometrically active atomic states (GAASs) of Be, B, C, N, O and Ne atoms that are in the first excited states with configurations sαpβ. These results reveal that as an intrinsic property of the wave function of atoms, the angle of the most probabl angular distribution of two-electron density is approximately equal to the bond angle of the molecule, which usually can be explained by the hybridization theory.

The significance of double substitutions in well-correlated electronic wave functions

The enhancement of the weighting of double substitutions in correlated wave functions is a very significant effect from including into a wave function the higher-level substitutions. The coupled cluster model seems quite effective at bringing about this enhancement and because of this it yields correlation energies in line with those obtained by variational configuration interaction explicitly involving higher-level substitutions. The enhancement of double substitutions as a prominent higher-order effect is demonstrated by calculations of the HF dipole moment curve, where this enhancement provides an important adjustment to the curve.

Variational configuration interaction methods and comparison with perturbation theory

A configuration interaction (Cl) procedure which includes all single and double substitutions from an unrestricted Hartree-Fock single determinant is described. This has the feature that Møller-Plesset perturbation results to second and third order are obtained in the first Cl iterative cycle. The procedure also avoids the necessity of a full two-electron integral transformation. A simple expression for correcting the final Cl energy for lack of size consistency is proposed. Finally, calculations on a series of small molecules are presented to compare these Cl methods with perturbation theory.

Some aspects of diagrammatic perturbation theory

Many-body perturbation theory, or the linked cluster diagrammatic representation of Rayleigh-Schrödinger perturbation theory, is demonstrated to arise from the variational configuration interaction procedure by elementary considerations of Löwdin's partitioning approach to perturbation theory. As a consequence, variational upper bounds to the energy, which arise from the inclusion of some “unlinked” terms, may be obtained from odd-order MBPT calculations and are useful for certain applications. A brief discussion of low-order correlation diagrams for second-order properties is also presented.

Transition probabilities found for M + CH4 reactions (M = zinc, copper)

AbstractTransition probabilities between the lowest energy levels of M + CH4 (M = Zn, Cu) reactions were obtained through nonadiabatic crossings using a modification of the Landau–Zener (L–Z) theory. Hartree Fock self consistent field (HF‐SCF) ab initio calculations were utilized to obtain the reaction pathways by means of the PSHF program, while pseudopotentials for representing the core–core and core‐valence interaction were applied. The correlation energy is taken into account by means of multireference variational and perturbative configuration interaction calculations to second order using CIPSI code. The variational space generated in iterative manner includes more than 250 determinants, while the perturbative space is about 3 × 107 configurations. The perturbative contribution is about 40% of the total correlation energy recovered. The time dependent L–Z theory was developed through the reaction coordinate r (distance). An extension of the latter theory to the reaction coordinate θ (angle) was used in this case. Then, the nonadiabatic crossings depend on both the angular velocity and the moment of inertia, among other things. The transition probability of the system HMCH3 (M = Zn, Cu) leading from one energy level to another is calculated through an avoided crossing. This method has been previously tested on gallium‐methane and gallium‐silane reactions for which the theoretical probability transitions between potential energy surfaces of gallium‐methane reactions agree with experimental quenching branching fractions with great accuracy. © 2008 Wiley Periodicals, Inc., 2008

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.

Structure and spectra of a confined HeH molecule

The influence of spatial confinement on the structure and spectra of the Rydberg HeH molecule is analysed at the level of the variational full configuration interaction approach. The confining potential is assumed to have cylindrical symmetry, with the symmetry axis of the potential overlapping with the molecular bond. In the direction perpendicular to the axis quadratic dependence of the potential on the electron coordinates is assumed. The influence of the confining potential on the form of the potential energy curves (in particular on the bond lengths), on the electronic spectra and on the ionization due to the confinement is studied in detail.