Multireference Configuration Interaction Method Research Articles

Mutual Neutralization in Collisions of Li+ with O−

The total and differential cross-sections and final state distribution for mutual neutralization in collisions of Li+ with O− were calculated using an ab initio quantum mechanical approach based on potential energy curves and non-adiabatic coupling elements computed with the multi-reference configuration interaction method. The final state distributions favored channels with excited oxygen states, indicating a strong effect of electron correlation, and the electron transfer could not be described by a simple one-electron exchange process.

Theoretical spin-orbit laser cooling for AlZn molecule.

A spin-orbit coupling electronic structure study of the AlZn molecule is conducted to investigate the molecular properties of the low-lying electronic states and their feasibility toward direct laser cooling. This study uses the complete active-space self-consistent field level of theory, followed by the multireference configuration interaction method with Davidson correction (+Q). The potential energy and dipole moment curves and the spectroscopic constants are computed for the low-lying doublet and quartet electronic states in the 2S+1Λ± and Ω(±) representations. The transition dipole moments, the Franck-Condon factors, the Einstein coefficient, the radiative lifetimes, the vibrational branching ratio, and the slowing distance are determined between the lowest spin-orbit bound electronic states. These results show that the molecule AlZn has a high potential for laser cooling through the X2Π1/2 → (2)2Π1/2 transition by utilizing four lasers at a wavelength in the ultraviolet region, reaching a sub-microkelvin temperature limit.

Formation of S2 species in different redox states by radiative association in atomic and ionic collisions

Radiative associations for formations of the S2, S2+ and S2- molecular species during atomic collisions S(3Pu) + S(3Pu), S(3Pu) + S+(4Su) and S(3Pu) + S-(2Pu) are investigated. The adiabatic potential energy curves (PECs) and spin-allowed transition dipole moments (TDMs) are obtained by the internally contracted multireference configuration interaction method with the Davidson correction (icMRCI+Q). A number of PECs and TDMs are chosen to calculate the corresponding cross-sections and rate coefficients of radiative associations. The calculated rate coefficients are valid for the temperatures from 100 to 16000 K and fitted to the analytical function according to the three-parameter Arrhenius–Kooij formula. These results indicate that transitions originating in the ΔΛ=0 selection rule are the main contributors for the radiative association process. The present study can elucidate the further understanding the radiative association, which plays an important role in the formation and evolution of the S2, S2+ and S2- molecules.

Non-adiabatic dynamics studies of the C+(2P1/2, 3/2) + H2 reaction: Based on global diabatic potential energy surfaces of CH2.

Global diabatic potential energy surfaces (PESs) of CH2+ are constructed using the neural network method with a specific function based on 18 213 abinitio points. The multi-reference configuration interaction method with the aug-cc-pVQZ basis set is adopted to perform the abinitio calculations. The topographical properties of the diabatic PESs are examined in detail. In general, the diabatic PESs provide an accurate quasi-diabatic representation. To validate the diabatic PESs, the dynamics studies of the C+(2P1/2, 3/2) + H2 (v0 = 0, j0 = 0) → H + CH+(X1Σ+) reaction are performed using the time-dependent wave packet method. The reaction probabilities, integral cross sections, differential cross sections, and rate constants are calculated and compared with the experimental and theoretical results. Non-adiabatic dynamics results are in good agreement with experimental data. In addition, the non-adiabatic effect in the C+(2P1/2, 3/2) + H2 reaction is significant due to the non-adiabatic results being obviously larger than adiabatic values. The reasonable non-adiabatic dynamics results indicate that present diabatic PESs can be recommended for any type of dynamics study.

A theoretical study on excited-state dynamical properties and laser cooling of zinc monohydride including spin-orbit couplings.

By means of highly accurate ab initio and dynamical calculations, we identify a suitable laser cooling candidate that contains a transition metal element, namely zinc monohydride (ZnH). The internally contracted multireference configuration interaction method is employed to compute the five lowest-lying Λ-S states of ZnH with the spin-orbit coupling effects included, and very good agreement is obtained between our calculated and experimental spectroscopic data. Our findings show that the position of crossing point of the A2Π and B2Σ+ states of ZnH is above the v' = 2 vibrational level of the A2Π state indicating that the crossings with higher electronic states will have no effect on laser cooling. Hence, we construct a feasible laser-cooling scheme for ZnH using five lasers based on the A2Π1/2 → X2Σ+ 1/2 transition, which features a large vibrational branching ratio R 00 (0.8458), a large number of scattered photons (9.8 × 103) and an extremely short radiative lifetime (64ns). The present work demonstrates the importance of electronic state crossings and spin-orbit couplings in the study of molecular laser cooling.

Theoretical investigation of the electronic structure of the Rhodium Halides molecules RhF and RhCl with dipole moment calculation

The current study involves an ab initio exploration of the ground and low-lying excited electronic states of the rhodium halide molecules RhF and RhCl using the complete active space self-consistent field (CASSCF) with multireference configuration interaction (MRCI+Q) method including single and double excitations and with Davidson corrections. We investigated the potential energy curves, the transition and permanent electric dipole moments, the electronic energy relative to the ground state Te, the harmonic frequency ωe, the internuclear distance Re, and the rotational constant Be corresponding to each of the bounded states. Our findings demonstrate good agreement with the available experimental data. Notably, this work represents the inaugural theoretical investigation of the excited states of RhF and RhCl molecules, identifying the ground state of both to be X3Π, as observed in the sole two experimental investigations.

A Globally Accurate Neural Network Potential Energy Surface and Quantum Dynamics Studies on Be+(2S) + H2/D2 → BeH+/BeD+ + H/D Reactions.

Chemical reactions between Be+ ions and H2 molecules have significance in the fields of ultracold chemistry and astrophysics, but the corresponding dynamics studies on the ground-state reaction have not been reported because of the lack of a global potential energy surface (PES). Herein, a globally accurate ground-state BeH2+ PES is constructed using the neural network model based on 18,657 ab initio points calculated by the multi-reference configuration interaction method with the aug-cc-PVQZ basis set. On the newly constructed PES, the state-to-state quantum dynamics calculations of the Be+(2S) + H2(v0 = 0; j0 = 0) and Be+(2S) + D2(v0 = 0; j0 = 0) reactions are performed using the time-dependent wave packet method. The calculated results suggest that the two reactions are dominated by the complex-forming mechanism and the direct abstraction process at relatively low and high collision energies, respectively, and the isotope substitution has little effect on the reaction dynamics characteristics. The new PES can be used to further study the reaction dynamics of the BeH2+ system, such as the effects of rovibrational excitations and alignment of reactant molecules, and the present dynamics data could provide an important reference for further experimental studies at a finer level.

Quadruple bonds in MoC: Accurate calculations and precise measurement of the dissociation energy of low-lying states of MoC.

In the present work, the electronic structure and chemical bonding of the MoC X3Σ- ground state and the six lowest excited states, A3Δ, a1Γ, b5Σ-, c1Δ, d1Σ+, and e5Π, have been investigated in detail using multireference configuration interaction methods and basis sets, including relativistic effective core potentials. In addition, scalar relativistic effects have been considered in the second order Douglas-Kroll-Hess approximation, while spin-orbit coupling has also been calculated. Five of the investigated states, X3Σ-, A3Δ, a1Γ, c1Δ, and d1Σ+, present quadruple σ2σ2π2π2 bonds. Experimentally, the predissociation threshold of MoC was measured using resonant two-photon ionization spectroscopy, allowing for a precise measurement of the dissociation energy of the ground state. Theoretically, the complete basis set limit of the calculated dissociation energy with respect to the atomic ground state products, including corrections for scalar relativistic effects, De(D0), is computed as 5.13(5.06) eV, in excellent agreement with our measured value of D0(MoC) of 5.136(5) eV. Furthermore, the calculated dissociation energies of the states having quadruple bonds with respect to their adiabatic atomic products range from 6.22 to 7.23eV. The excited electronic states A3Δ2 and c1Δ2 are calculated to lie at 3899 and 8057 cm-1, also in excellent agreement with the experimental values of DaBell et al., 4002.5 and 7834 cm-1, respectively.

Quantum chemical calculations of electron affinities of alkaline earth metal atoms (Ca, Sr, Ba, and Ra)

We performed high-level ab initio quantum chemical calculations, incorporating higher-order excitations, spin–orbit coupling (SOC), and the Gaunt interaction, to calculate the electron affinities (EAs) of alkaline earth (AE) metal atoms (Ca, Sr, Ba, and Ra), which are notably small. The coupled-cluster singles and doubles with perturbative triples [CCSD(T)] method is insufficient to accurately calculate the EAs of AE metal atoms. Higher-order excitations proved crucial, with the coupled-cluster singles, doubles, and triples with perturbative quadruples [CCSDT(2)Q] method effectively capturing dynamic electron correlation effects. The contributions of SOC (ΔESOs) to the EAs calculated using the multireference configuration interaction method with the Davidson correction, including SOC, positively enhance the EAs; however, these contributions are overestimated. The Dirac–Hartree–Fock (DHF)-CCSD(T) method addresses this overestimation and provides reasonable values for ΔESO (ΔESO−D). Employing additional sets of diffuse and core–valence correlation basis sets is critical for accurately calculating the EAs of AE metal atoms. The contributions of the Gaunt interaction (ΔEGaunt) to the EAs of AE metal atoms are negligible. Notably, the CCSDT(2)Q with the complete basis set limit + ΔESO−D + ΔEGaunt produced EA values for Ca, Sr, and Ba that closely aligned with experimental data and achieved accuracy exceeding the chemical accuracy. Based on our findings, the accurately proposed EA for Ra is 9.88 kJ/mol.

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.

Theoretical study of low-lying electronic states spectra and transition properties of BeS molecule

There are only limited theoretical results published on the transition properties of the X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, and c3Δ states of BeS, and even some of the states have no theoretical and experimental reports on the relevant aspects of these transitions. Therefore, we derived these transition properties in this study. The potential energy curves of X1Σ+, A1Π, B1Σ+, C1Δ, D1Σ−, E1Δ, a3Π, b3Σ+, c3Δ, d3Σ−, and e3Σ− states of the BeS molecule with their Ω states and the transition dipole moments between them were calculated by the complete active space self-consistent field method, followed by the internally contracted multireference configuration interaction method. For the accurate computation of the transition properties, scalar relativistic corrections and core–valence correlation were considered. The radiative lifetimes were approximately 10−6 s for the A1Π and b3Σ+ states, 10−7 s for the E1Δ state, 10−7–10−8 s for the C1Δ and D1Σ− states, and 10−8 s for the B1Σ+, c3Δ, and e3Σ− states. The transition properties of the seven Ω states generated by the X1Σ+, A1Π, B1Σ+, and a3Π electronic states, including several electric dipole-forbidden transitions were researched. In particular, the B1Σ+ 0+–X1Σ+ 0+, B1Σ+ 0+–A1Π1, and A1Π1–X1Σ+ 0+ systems have strong transitions. In this paper, the radiative lifetimes of A1Π1, B1Σ+ 0+, a3Π0−, a3Π0+, and a3Π1 electronic states were also computed. For the A1Π1, B1Σ+ 0+, and a3Π1 states, the distribution of the radiation lifetime with the rotational angular momentum quantum number J at 0 ≤ υ ≤ 15 and J ≤ 70 was evaluated. It is expected that the outcome of the calculations in this paper can contribute some meaningful guidelines for conducting further theoretical and experimental investigations.

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.

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.

Fourier-transform spectroscopy and global deperturbation treatment of the A1Σu+ and b3Πu states of K2 in the entire bound energy range.

Rotationally resolved Fourier-transform spectra of laser-induced fluorescence A1Σu+∼b3Πu→X1Σg+ of K2 molecules were recorded and analyzed, yielding 4053 term values of the spin-orbit (SO) coupled A ∼ b complex of the 39K2 isotopologue with ∼0.01 cm-1 accuracy. Their compilation with 1739 term values from previously published sources allowed them to cover the energy range [9955, 17 436] cm-1 from the bottom of the lower-lying b3Πu state up to the vicinity of the atomic asymptote 4s2S12 + 4p2P12, with a rotational quantum number J ∈ [0, 149]. The experimental data were processed by a direct 6 × 6 coupled-channel (CC) deperturbation treatment, which accounted explicitly for both SO and electronic-rotational interactions between all six e-symmetry states: A1Σu+(0u+), b3Πu(0u+,1u,2u), c3Σu(1u), and B1Πu(1u). The initial parameters of the global deperturbation model have been estimated in the framework of abinitio electronic structure calculations applying multi-reference configuration-interaction and coupled-clusters methods. The interatomic potentials analytically defined for A and b states, as well as SO-splitting of the triplet b state and A ∼ b SO-coupling functions, have been particularly refined to fit the 5792 term values of the 39K2 isotopologue, whereas the rest parameters were fixed on their abinitio values. The resulting mass-invariant parameters of the 6 × 6 CC model reproduced the overall rovibronic term energies of the A ∼ b complex of 39K2 with accuracy, which is well within the experimental errors. The quality of the deperturbation analysis was independently confirmed by comparison with the present obtained 705 and 14 term values of respective 39K41K and 41K2 isotopologues, as well as by agreement between measured and predicted relative intensity distributions in long A ∼ b → X(vX) band progressions. This deperturbation analysis provided the refined dissociation energy Tdis = 17 474.569(5) cm-1 and the long-range coefficient C3Σ = 5.501(4) × 105 cm-1 Å3 relevant to the non-relativistic atomic limit 4s + 4p. The derived Tdis yielded the accurate well depth De = 4450.910(5) cm-1 for the ground X1Σg+ state, whereas the new C3Σ value yielded the improved estimates for atomic K(4p2P12;32) radiative lifetimes, τ12 = 26.67(3) and τ32 = 26.32(3) ns.

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.