Multireference Configuration Interaction Research Articles

Quantum study of the CH3+ photodissociation in full-dimensional neural network potential energy surfaces.

C H 3 + , a cornerstone intermediate in interstellar chemistry, has recently been detected for the first time by using the James Webb Space Telescope. The photodissociation of this ion is studied here. Accurate explicitly correlated multi-reference configuration interaction abinitio calculations are done, and full-dimensional potential energy surfaces are developed for the three lower electronic states, with a fundamental invariant neural network method. The photodissociation cross section is calculated using a full-dimensional quantum wave packet method in heliocentric Radau coordinates. The wave packet is represented in angular and radial grids, allowing us to reduce the number of points physically accessible, requiring to push up the spurious states appearing when evaluating the angular kinetic terms, through projection technique. The photodissociation spectra, when employed in astrochemical models to simulate the conditions of the Orion bar, result in a lesser destruction of CH3+ compared to that obtained when utilizing the recommended values in the kinetic database for astrochemistry.

Analytic Nuclear Gradients for Complete Active Space Linearized Pair-Density Functional Theory.

Accurately modeling photochemical reactions is difficult due to the presence of conical intersections and locally avoided crossings, as well as the inherently multiconfigurational character of excited states. As such, one needs a multistate method that incorporates state interaction in order to accurately model the potential energy surface at all nuclear coordinates. The recently developed linearized pair-density functional theory (L-PDFT) is a multistate extension of multiconfiguration PDFT, and it has been shown to be a cost-effective post-MCSCF method (as compared to more traditional and expensive multireference many-body perturbation methods or multireference configuration interaction methods) that can accurately model potential energy surfaces in regions of strong nuclear-electronic coupling in addition to accurately predicting Franck-Condon vertical excitations. In this paper, we report the derivation of analytic gradients for L-PDFT and their implementation in the PySCF-forge software, and we illustrate the utility of these gradients for predicting ground- and excited-state equilibrium geometries and adiabatic excitation energies for formaldehyde, s-trans-butadiene, phenol, and cytosine.

Electronic structure, spectroscopy and photophysics of rubidium mono-sulphide

We investigated the nineteen first electronic states of the RbS diatomic using post Hartree-Fock configuration interaction methods at the internally contracted multi-reference configuration interaction (MRCI+(Q)) level. We thus mapped their respective potential energy curves with and without considering spin-orbit effects. After nuclear motion treatments, we derived their equilibrium distances, rotational and vibrational constants, and dissociation and electronic excitation energies. Moreover, an evaluation of the dipole moments of RbS was conducted, which in turn were used to evaluate the radiative lifetimes of the vibrational levels of RbS (X2П and A2Σ+) states. Computations show that spin-orbit interactions are important and cannot be omitted. Afterwards, and utilizing the sum rule approximation and the Franck–Condon factors, we computed both the bound-bound contributions and the bound-free terms. Our findings suggest that RbS exhibits intriguing characteristics suitable for laser cooling experiments. In sum, this work contributes to the understanding in-depth of the spectroscopy of RbS and predicts its use as a promising molecular system for laser cooling applications.

Ab initio spectroscopic studies of AlF and AlCl molecules

In this work, we report the results from our spectroscopic study on AlF and AlCl molecules. We carry out detailed electronic structure calculations in both the molecules, including obtaining the potential energy surfaces of the [Formula: see text] ground electronic state and some of the low-lying excited electronic states belonging to [Formula: see text] and [Formula: see text] symmetries. This is followed by evaluating the spectroscopic constants and molecular properties such as electric dipole moments and electric quadrupole moments. Throughout, we employ the multi-reference configuration interaction method and work with high-quality quadruple zeta basis sets. Further, transition dipole moments between the ground electronic state and singlet excited states are also studied. The relevant vibrational parameters are computed by solving the vibrational Schrödinger equation. Subsequently, the vibrational energy spacings and transition dipole moments between the vibrational levels belonging to the same electronic states are used to evaluate the spontaneous and black-body radiation-induced transition rates, followed by computing the lifetimes. Finally, the energy differences between rotational levels belonging to different vibrational levels and within an electronic state as well as the Einstein coefficients are reported.

Ab Initio Study on Electronic Excited States of Monochlorosilylene.

We perform a high-level ab initio study on 20 electronic states of monochlorosilylene (HSiCl) using an internally contracted multireference configuration interaction method including Davidson correction (icMRCI+Q). The spin-orbit coupling (SOC) effect is investigated, leading to splitting of the 20 spin-orbit-free states into 50 spin-orbit-coupled states. Vertical transition energies, oscillator strengths, and potential energy curves are presented with and without considering the SOC effect. Analysis indicates that the SOC effect plays an important role, especially for the high-lying excited states of HSiCl. The state interaction and the dynamics of the electronic states of HSiCl in the ultraviolet region are discussed based on our calculation results. Our study paves the way to understanding the behavior of electronic excited states of monochlorosilylene.

Predissociation dynamics of the hydroxyl radical (OH) based on a five-state spectroscopic model.

Multi-reference configuration interaction potential energy curves (PECs) and spin-orbit couplings for the X 2Π, A 2Σ+, 1 2Σ-, 1 4Σ-, and 1 4Π states of OH are computed and refined against empirical energy levels and transitions to produce a spectroscopic model. Predissociation lifetimes are determined by discretizing continuum states in the variational method nuclear motion calculation by restricting the calculation to a finite range of internuclear separations. Varying this range gives a series of avoided crossings between quasi-bound states associated with the A 2Σ+ and continuum states, from which predissociation lifetimes are extracted. 424 quasi-bound A 2Σ+ state rovibronic energy levels are analyzed, and 374 predissociation lifetimes are produced, offering good coverage of the predissociation region. Agreement with measured lifetimes is satisfactory, and a majority of computed results were within experimental uncertainty. A previously unreported A 2Σ+ state predissociation channel that goes via X 2Π is identified in the calculations. A Python package, binSLT, produced to calculate predissociation lifetimes, associated line broadening parameters, and lifetime uncertainties is made available. The PECs and other curves from this work will be used to produce a rovibronic ExoMol line list and temperature-dependent photodissociation cross sections for the hydroxyl radical.

High-Resolution Rovibronic Cross Sections of the MgH+ Molecular Cation.

The high-resolution rovibronic line lists of the MgH+ molecular cation are presented in our work. The potential energy curves are calculated by the method of multireference configuration interaction and Davidson correction (MRCI+Q) with the spin-orbit coupling (SOC) effect. Spectroscopy constants are fitted and the results are in good agreement with experiments, ensuring the accuracy of the electronic structure. On account of potential energy curves and transition dipole moments, the Franck-Condon factors and Einstein coefficients of transition are obtained. These calculations are used to obtain an accurate partition functions and line lists for molecules. Using the partition functions and line lists, the absorption cross-sections under different temperatures and pressures were simulated. Our work could provide some theoretical insights into solar and cold planet spectrum.

Multiexcitonic and optically bright states in subunits of pentacene crystals: A hybrid DFT/MRCI and molecular mechanics study.

A hybrid quantum mechanics/molecular mechanics setup was used to model electronically excited pentacene in the crystal phase. Particularly interesting in the context of singlet fission (SF) is the energetic location of the antiferromagnetically coupled multiexcitonic singlet state, 1(TT), and the ferromagnetically coupled analog in relation to the optically bright singlet state. To provide photophysical properties of the accessible spin manifold, combined density functional theory and multi-reference configuration interaction calculations were performed on pentacene dimers and a trimer, electrostatically embedded in the crystal. The likelihood of a quintet intermediate in the SF process was estimated by computing singlet-quintet electron spin-spin couplings employing the Breit-Pauli Hamiltonian. The performance of the applied methods was assessed on the pentacene monomer. The character of the optically bright state and the energetic location of the 1(TT) state depend strongly on the relative orientation of the pentacene units. In the V-shaped dimers and in the trimer, the optically bright state is dominated by local and charge transfer (CT) excitations, with admixtures of doubly excited configurations. The CT excitations gain weight upon geometry relaxation, thus supporting a CT-mediated SF mechanism as the primary step of the SF process. For the slip-stacked dimer, the energetic order of the bright and the 1(TT) states swaps upon geometry relaxation, indicating strong nonadiabatic coupling close to the Franck-Condon region-a prerequisite for a coherent SF process. The multiexcitonic singlet, triplet, and quintet states are energetically too far apart and their spin-spin couplings are too small to bring about a noteworthy multiplicity mixing.

Transition probabilities and radiative lifetimes of C[formula omitted]: A high level theoretical investigation

Dicarbon species are of particular interest within the physical chemistry community. However, contrary to neutral C2, the theory of electronic structure and spectra concerning C2− ions is not well-established. To address this gap in information, high-level multireference configuration interaction (MRCI) calculations have been performed, and new potential energy curves for fourteen low-lying states of C2− are reported. The best estimate for the ground dissociation energy is 64,720 cm−1 at the MRCI+Q/AV5Z level of theory. The first excited state, A2Πu, lies at 3,836 cm−1 (Re = 2.4829 a0 and ωe = 1649 cm−1). The infrared A2Πu − X2Σg+ transition has Einstein coefficients of the order of 103–104 s−1. The lifetime of the A2Πu state is given in microseconds. For the B2Σu+ state, it was calculated τ0≈ 78 ns in good accord with the experimental value of 77 ± 8 ns. The a4Σu+ state is placed at an excitation energy of 32,369 cm−1, much higher than expected by experimentalists (19,448 cm−1). The spin-forbidden transitions a4Σu+ − X2Σg+ are strong enough to be detected experimentally (A04≈ 3 × 106 s−1). The 14Πg − a4Σu+ transitions are more concentrated in the IR region. The radiative lifetime of 14Πg is computed to be 12μs. There is no doubt that the current data considerably enhance our understanding of the spectroscopy of C2−.

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone.

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200fs, with dissociation events finished after 300fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Theoretical Investigation on Electronic Excited States of the HSO Radical.

HSO radicals play an important role in the photochemical processes in combustion, the atmosphere, and the interstellar medium. In this work, we perform a high-level ab initio study on the electronic excited states of HSO using the internally contracted multireference configuration interaction methods including Davidson correction (icMRCI + Q) in combination with the correlation-consistent basis sets. The molecular geometries, vertical transition energies, oscillator strengths, and electronic configurations of 19 electronic states of HSO are computed. The electronic potential energy curves of HSO along the bond lengths and bond angles are presented. Based on our calculations, the interactions between the electronic states involved in the ultraviolet region and the mechanism of photodissociation are discussed, which will lay a foundation for revealing the dissociation dynamics of gas-phase HSO molecules in outer space and the earth's atmosphere.

Transition properties of the spin- forbidden a4Π-X2Π systems in the NO, PO and PS molecules

The potential energy curves (PECs) for six low-lying states corresponding to the first dissociation limit (4Su+3Pg) of the NO, PO, and PS molecules are calculated by the multireference configuration interaction (MRCI) method. The X2Π -a4Π band is the focus of this work. By introducing the spin-orbit coupling (SOC) with Breit-Pauli operator via state-interacting technique, the PECs and wavefunctions compositions of Ω states are obtained. Based on the Λ-S states composition of the corresponding Ω states and the calculated electric-dipole transition moments between Λ-S state, we present intensity of the spin-forbidden quartet-doublet bands. Spectroscopic constants for all sub-bands of the a24Π3/2, a34Π1/2, a44Π1/2→X12Π1/2 and a14Π5/2, a24Π3/2, a34Π1/2, a44Π1/2→X22Π3/2 systems of the NO, PO, and PS are estimated. A set of transition parameters of these sub-bands are given. The present results are supposed to provide a significant supplement for the spin-forbidden a4Π→X2Π band origins of the astrophysically important NO, PO, and PS molecules.

Electronic structure with spin-orbit coupling effect of HfH molecule for laser cooling investigations

The electronic structure, including the spin–orbit coupling effect of the HfH molecule, has been studied to determine if it can be cooled through Doppler and Sysphus laser cooling techniques. The multi-reference configuration interaction plus Davidson correction (MRCI + Q) method has been used to calculate its potential energy curves (P.E.C.s) in the Ω(±) and 2s+1Ʌ(+/-) representation. The spectroscopic constants Te, Re, ωe, Be, αe, the dipole moment µe, and the dissociation energies De agree very well with previously published work. In addition, we present in this work twenty new doublet and quartet states in the Ω(±) representation. The electronic transition dipole moment curves (TDMCs) between the lowest-lying electronic states have been investigated for the Δ - Π, Π - ∑+ and Δ - Φ transitions among specific Ω(±) states. The Franck-Condon factors (FCFs), the Einstein coefficient of spontaneous emission Aν′ν, and the radiative lifetime τ have been computed for the investigated transitions. In addition, properties of the molecules' electronic and vibrational states, such as the static dipole moment curves (D.M.C.s), the ionic character fionic, and the rovibrational constants are calculated. We deduce from our results that the HfH molecule is indeed a laser-cooling candidate that can reach a temperature as low as the nK regime. We present a complementary scheme with suitable experimental parameters. These results can be of great interest to experimental spectroscopists interested in ultracold diatomic molecules and their applications.

Characterization of low-lying electronic states of diatomic sodium bismuthide cation including the spin-orbit coupling effect

We present a high-level ab initio investigation of the diatomic sodium bismuth (NaBi+), which is a hitherto experimentally unknown species. The explicitly correlated multireference configuration interaction method is used to calculate energy points of thirteen low-lying Λ-S electron states associated with five dissociation limits. Detailed information on structural features, electronic characters, and spectroscopic constants is acquired. Our calculated relative energies between each of the interested higher dissociation limits and the lowest one for NaBi+, as well as splittings of energy levels for Bi, agree well with experimental data. Besides, we have identified and discussed the transition properties of bands from excited Ω states to the ground one, including transition dipole moments, Einstein coefficients, Franck-Condon factors, vibrational branching ratios, and radiative lifetimes. The extent of perturbations originating from the spin-orbit coupling effect to the present species is quantified through discussions on term values of spin-orbit matrix elements, and the spin-orbit coupling effect is proved to have introduced a significant effect to the low-lying electronic states of NaBi+.

Renormalized-Residue-Based Multireference Configuration Interaction Method for Strongly Correlated Systems.

The implementation of multireference configuration interaction (MRCI) methods in quantum systems with large active spaces is hindered by the expansion of configuration bases or the intricate handling of reduced density matrices (RDMs). In this work, we present a spin-adapted renormalized-residue-based MRCI (RR-MRCI) approach that leverages renormalized residues to effectively capture the entanglement between active and inactive orbitals. This approach is reinforced by a novel efficient algorithm, which also facilitates an efficient deployment of spin-adapted matrix product state MRCI (MPS-MRCI). The RR-MRCI framework possesses several advantages: (1) It considers the orbital entanglement and utilizes highly compressed MPS structure, improving computational accuracy and efficiency compared with internally contracted (ic) MRCI. (2) Utilizing small-sized buffer environments of a few external orbitals as probes based on quantum information theory, it enhances computational efficiency over MPS-MRCI and offers potential application to large molecular systems. (3) The RR framework can be implemented in conjunction with ic-MRCI, eliminating the need for high-rank RDMs, by using distinct renormalized residues. We evaluated this method across nine diverse molecular systems, including Cu2O22+ with an active space of (24e,24o) and two complexes of lanthanide and actinide with active space (38e,36o), demonstrating the method's versatility and efficacy.

Coupled 3D (J ≥ 0) Time-Dependent Wave Packet Calculation for the F + H2 Reaction on Accurate Ab Initio Multi-State Diabatic Potential Energy Surfaces.

We had calculated adiabatic potential energy surfaces (PESs), nonadiabatic, and spin-orbit (SO) coupling terms among the lowest three electronic states (12A', 22A', and 12A″) of the F + H2 system using the multireference configuration interaction (MRCI) level of theory, and the adiabatic-to-diabatic transformation equations were solved to formulate the diabatic Hamiltonian matrix [J. Chem. Phys. 2020, 153, 174301] for the entire region of the nuclear configuration space. The accuracy of such diabatic PESs is explored by performing scattering calculations to evaluate integral cross sections (ICSs) and rate constants. The nonadiabatic and SO effects are studied by utilizing coupled 3D time-dependent wave packet formalism with zero and nonzero total angular momentum on multiple adiabatic/diabatic surfaces calculation. We depict the convergence profiles of reaction probabilities for the reactive as well as nonreactive processes on various electronic states at different collision energies with respect to total angular momentum including all helicity quantum numbers. Finally, total ICSs are calculated as functions of collision energies for the initial rovibrational state (v = 0, j = 0) of the H2 molecule along with the temperature-dependent rate coefficient, where those quantities are compared with previous theoretical and experimental results.

Electronic structure of ground and low-lying excited states of BaLi+ molecular ion: spin-orbit effect, radiative lifetimes and Franck-Condon factor

The study of BaLi+ and its reactivity plays a crucial role in advancing our understanding of chemical bonding or reaction mechanisms. The aim of this work is to represent a complete and extended theoretical study of BaLi+ molecular ion including ground and highly excited electronic states of 1,3Σ, 1,3Π and 1,3Δ symmetries, dissociated to the first seven dissociation limits. The corresponding potential energy curves (PECs), permanent and transition dipole moments have been investigated. These calculations were performed using the multireference configuration interaction (MRCI) method in combination with optimized basis sets and non-empirical pseudopotentials (ECP) for both Ba and Li atoms. Afterwards, the spin–orbit (SO) operator is incorporated in valence MRCI calculation using optimized relativistic spin–orbit pseudopotentials and 16 Ω states are generated and splitted into Λ-S states. The SO effect gives rise to a more complicated structure of electronic states presented in PEC and permanent and transition dipole moments. Nonadiabatic coupling matrix elements between the five lowest 1Σ+ states are also presented for the nonrelativistic results. Based on the vibrational radiative lifetime and Franck–Condon calculation, the possibilities of laser cooling of this system have been also discussed.

Spin-Adapted Externally Contracted Multireference Configuration Interaction Method Based on Selected Reference Configurations.

As one kind of approximation of the full configuration interaction solution, the selected configuration interaction (sCI) methods have been shown to be valuable for large active spaces. However, the inclusion of dynamic correlation beyond large active spaces is necessary for more quantitative results. Since the sCI wave function can provide a compact reference for multireference methods, previously, we proposed an externally contracted multireference configuration interaction method using the sCI reference reconstructed from the density matrix renormalization group wave function [J. Chem. Theory Comput. 2018, 14, 4747-4755]. The DMRG2sCI-EC-MRCI method is promising for dealing with more than 30 active orbitals and large basis sets. However, it suffers from two drawbacks: spin contamination and low efficiency when using Slater determinant bases. To solve these problems, in this work, we adopt configuration state function bases and introduce a new algorithm based on the hybrid of tree structure for convenient configuration space management and the graphical unitary group approach for efficient matrix element calculation. The test calculation of naphthalene shows that the spin-adapted version could achieve a speed-up of 6.0 compared with the previous version based on the Slater determinant. Examples of dinuclear copper(II) compound as well as Ln(III) and An(III) complexes show that the sCI-EC-MRCI can give quantitatively accurate results by including dynamic correlation over sCI for systems with large active spaces and basis sets.

The radiative association of PO/PH+ and the photodissociation of PH+

The potential energy curves (PECs) and transition dipole moments (TDMs) of PH+ and PO are computed with the multireference configuration interaction method, and the cross-sections for the radiative association (RA) of PH+ and PO, which is the most efficient way to form the ground states, are presented via the quantum mechanical (QM) theory and computed using ab initio molecular data. The thermal rate coefficients are also expressed and fitted with the standard formula kT=AT300αe−βT in the range of 10 K–15,000 K. Meanwhile, the photodissociation, that is the inverse process of RA for PH+, is also studied, including eight photodissociation channels for the computation of state-resolved cross-sections. Careful comparisons with the Leiden Observatory database are made. Considering the cross-sections mentioned above, the local thermodynamic equilibrium cross-sections at the temperatures of 0, 500, 1,000, and 2,000 K are also shown. We expect the results to be helpful for studies of phosphorus chemistry in the interstellar medium and planetary atmospheres.

The CuTe Molecule: Theoretical investigation of the electronic structure and dipole moments of the ground and lowest excited states with rovibrational calculations

The multireference configuration interaction calculation MRSDCI (with Davidson correction) has been performed to investigate the potential energy curves, the transition electronic energies Te, the spectroscopic constants (Re, ωe and Be), the transition and permanent dipole moments, and the vibrational levels corresponding to the ground and 18 excited electronic states of the molecule CuTe in the representation 2S+1Λ(+/-) (neglecting the spin–orbit effects), whereas the PECs and the spectroscopic constants have been calculated for 27 states in the representation Ω(+/-) [including the spin–orbit (SO) effects]. The ground state equilibrium bond length and the vibrational frequency have also been investigated using the density functional theory (DFT), where different density functionals with different basis sets have been tested. This study represents the first theoretical study of the excited states of the CuTe molecule. Comparison of the present results with the available experimental ones shows an overall satisfying agreement.