Multireference Configuration Interaction Method Research Articles

Near-thermo-neutral electron recombination of titanium oxide ions.

While the dissociative recombination (DR) of ground-state molecular ions with low-energy free electrons is generally known to be exothermic, it has been predicted to be endothermic for a class of transition-metal oxide ions. To understand this unusual case, the electron recombination of titanium oxide ions (TiO+) with electrons has been experimentally investigated using the Cryogenic Storage Ring. In its low radiation field, the TiO+ ions relax internally to low rotational excitation (≲100 K). Under controlled collision energies down to ∼2 meV within the merged electron and ion beam configuration, fragment imaging has been applied to determine the kinetic energy released to Ti and O neutral reaction products. Detailed analysis of the fragment imaging data considering the reactant and product excitation channels reveals an endothermicity for the TiO+ dissociative electron recombination of (+4 ± 10) meV. This result improves the accuracy of the energy balance by a factor of 7 compared to that found indirectly from hitherto known molecular properties. Conversely, the present endothermicity yields improved dissociation energy values for D0(TiO) = (6.824 ± 0.010)eV and D0(TiO+) = (6.832 ± 0.010)eV. All thermochemistry values were compared to new coupled-cluster calculations and found to be in good agreement. Moreover, absolute rate coefficients for the electron recombination of rotationally relaxed ions have been measured, yielding an upper limit of 1 × 10-7 cm3 s-1 for typical conditions of cold astrophysical media. Strong variation of the DR rate with the TiO+ internal excitation is predicted. Furthermore, potential energy curves for TiO+ and TiO have been calculated using a multi-reference configuration interaction method to constrain quantum-dynamical paths driving the observed TiO+ electron recombination.

Theoretical study of low-lying electronic states of AgH including spin-orbit coupling

High-level ab initio calculation of silver hydride (AgH) is performed by utilizing the internally contracted multi-reference configuration interaction plus Davidson correction method. A total of 6 Λ-S states and 11 Ω states from low-lying electronic states are computed in consideration of the spin-orbit coupling (SOC). The spectroscopic constants of bound states are determined and are in good agreement with the results of the available literature. A large aug-cc-pwCV5Z-PP basis set for Ag atom is applied during the calculations. The transition dipole moment (TDM) of spin forbidden transition between different multiplicity, caused by SOC effect, are computed based on Breit-Pauli operator. Particularly, the TDM of spin forbidden transitions between triplet aʹ3Σ+, a3Π, bʹ3Σ+ and singlet X1Σ+, A1Σ+, C1Π is studied and discussed. Finally, the interference of laser directly cooling by intermediate aʹ3Σ+ states due to SOC was investigated based on the obtained TDM parameters. It proves that the perturbation from aʹ3Σ+ state could be neglected in the laser cooling process.

R2022: A DFT/MRCI Ansatz with Improved Performance for Double Excitations

A reformulation of the combined density functional theory and multireference configuration interaction method (DFT/MRCI) is presented. Expressions for ab initio matrix elements are used to derive correction terms for a new effective Hamiltonian. On the example of diatomic carbon, the correction terms are derived, focusing on the doubly excited 1Δg state, which was problematic in previous formulations of the method, as were double excitations in general. The derivation shows that a splitting of the parameters for intra- and interorbital interactions is necessary for a concise description of the underlying physics. Results for 1La and 1Lb states in polyacenes and 1Au and 1Ag states in mini-β-carotenoids suggest that the presented formulation is superior to former effective Hamiltonians. Furthermore, statistical analysis reveals that all the benefits of the previous DFT/MRCI Hamiltonians are retained. Consequently, the here presented formulation should be considered as the new standard for DFT/MRCI calculations.

Theoretical study of the I++I− mutual neutralization reaction

We have computed the cross sections of the mutual neutralization reaction between ${\mathrm{I}}^{+}$ and ${\mathrm{I}}^{\ensuremath{-}}$ for a collision energy varying from 0.001 eV to 50 eV. These cross sections were obtained using the adiabatic potential energy curves of the ${\mathrm{I}}_{2}$ system computed with a direct relativistic multireference configuration interaction method and a semiclassical approach (i.e., Landau-Zener surface hopping). We report the cross sections towards the following neutral states: $\text{I}(^{2}P_{3/2})+\text{I}{(}^{2}{P}_{3/2})$, $\text{I}{(}^{2}{P}_{3/2})+\text{I}{(}^{2}{P}_{1/2})$, $\text{I}{(}^{2}{P}_{1/2})+\text{I}{(}^{2}{P}_{1/2})$, and $\text{I}(5{p}^{4}6s)+\text{I}{(}^{2}{P}_{3/2})$. We also discuss the cross sections towards the following two excited ionic states: ${\text{I}}^{\ensuremath{-}}{(}^{1}{S}_{0})+{\text{I}}^{+}{(}^{3}{P}_{0})$ and ${\text{I}}^{\ensuremath{-}}{(}^{1}{S}_{0})+{\text{I}}^{+}{(}^{3}{D}_{2})$. The results of these calculations are in qualitative accordance with recent experimental measurements conducted in the Double ElectroStatic Ion Ring ExpEriment (DESIREE) in Stockholm. These results can be used to model iodine plasma kinetics and thus to improve our understanding of the latter.

Near-Infrared Transitions from the Singlet Excited States to the Ground Triplet State of the S2 Molecule

Intensity of transitions from the b1∑g+ and a1Δg states to the ground state X3∑g− in the near IR emission spectrum of the S2 molecule has been calculated by the multireference configuration interaction method taking into account spin-orbit coupling (SOC). The intensity of the b1∑g+ − X3∑g,Ms=±1− transition is largely determined by the spin interaction with the electromagnetic wave, which comes from the zero-field splitting of the ground X multiplet and the SOC-induced mixing between b and X3∑g,0− states. The Einstein coefficients for the experimentally detected 0−0, 0−1, 1−1 bands of the b1∑g+−X3∑g,Ms=±1− emission system are calculated in good agreement with observations. The Einstein coefficient of the a1∆g−X3∑g,Ms=±1− magnetic dipole transition is very low, being equal to 0.0014 s−1. Nonetheless, the weakest of all experimentally observed bands (the 0−0 band of the a-XMs=±1 transition) qualitatively corresponds to this calculation. Most importantly, we provide many other IR bands for magnetic dipole b1∑g+ − X3∑g,Ms=±1− and a1∆g−X3∑g,Ms=±1− transitions, which could be experimentally observable in the S2 transparency windows from a theoretical point of view. We hope that these results will contribute to the further experimental exploration of the magnetic infrared bands in the S2 dimer.

The state-to-state dynamics of the N + NH(3Σ−) → N2(X1 Σg +) + H reaction: based on a new global potential energy surface

A new global potential energy surface (PES) of the ground state of the HN2 system is built using the neural network method. The aug-cc-pVQZ basis set for the H atom, cc-pwCVQZ basis set for the N atom and multi-reference configuration interaction method are employed in the ab initio calculations. The topographic features of the PES are discussed and compared with available theoretical studies. In addition, the initial state (v 0 = 0, j 0 = 0) dynamic studies of the N + NH(3Σ−) → N2(X1 ) + H reaction are performed using a time-dependent wave packet method, based on the newly constructed PES. The dynamics properties, such as reaction probabilities, integral cross-sections, differential cross-sections, the rovibrational state distribution of product and rate constants, are calculated at the state-to-state level of theory and compared with available theoretical and experimental results. The differential cross-section indicates that the forward abstraction mechanism dominates the reaction with the increase of collision energy. Highlights A new global potential energy surface of the ground state of the HN2 system was constructed using the neural network method. Quantum state-resolved dynamical calculations for the N + NH(3Σ−)(v 0 = 0, j 0 = 0) → N2(X1 ) + H reaction were carried out using a time-dependent wave packet method based on the newly constructed potential energy surface. Some meaningful dynamic properties were reported and compared with available theoretical and experimental data.

Electron affinities and lowest triplet and singlet state properties of para-oligophenylenes (n = 3-5): theory and experiment.

We apply photodetachment-photoelectron spectroscopy to measure the electron affinities and the energetics of the lowest excited electronic states of the neutral molecules para-terphenyl (p3P), para-quaterphenyl (p4P) and para-quinquephenyl (p5P), including especially the triplet states below S1. The interpretation of the experimental data is based on the comparison to calculated 0-0 energies and Dyson norms, using density functional theory and multireference configuration interaction methods, as well as Franck-Condon patterns. The comparison between calculated and experimental vibrational fine-structures reveals a twisted benzoid-like molecular structure of the S0 ground state and nearly planar quinoid-like nuclear arrangements in the S1 and T1 excited states as well as in the D0 anion ground state. For all para-oligophenylenes (ppPs) in this series, at least two triplet states have been identified in the energy regime below the S1 state. The large optical S0-S1 cross sections of the ppPs are rationalised by the nodal structure of the molecular orbitals involved in the transition. The measured electron affinities range from 380 meV (p3P) over 620 meV (p4P) to 805 meV (p5P). A saturation of the electron binding energy with the increasing number of phenyl units is thus not yet in sight.

Non-radiative charge transfer process of proton impcating B atom

Electron transfer in heavy particle collisions, involving complicated electron correlation mechanisms, greatly affects the charge state balance in plasma, and is also one of important sources for X-ray radiation. Electron transfer cross section and rate coefficient are important atomic parameters required for the development of nuclear fusion plasma in the national defense industry. We systematically investigate the electron transfer process of proton impacting boron atom in an energy range of <inline-formula><tex-math id="M4">\begin{document}${10}^{-3}-{10}^{3}\;{\rm{e}}{\rm{V}}/{\rm{u}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230470_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="16-20230470_M4.png"/></alternatives></inline-formula> based on a fully quantum non-radiative molecular orbital close-coupling method. A total of 15 channels of electron transfer, excitation, and elastic scattering are obtained by using the multi-reference configuration interaction method, and the corresponding molecular energy of each channel is in good agreement with the experimental results. The phenomenon of avoiding crossing between the adiabatic potential energy curves of molecular states is obvious, which constituents the main pathway of electron transfer. The calculation shows that the electron transfer of the 2s orbital is dominated in the process of proton impacting boron atom, while the electron transfer of the 2p orbital contributes a little. In the low energy region, there are obvious quantum resonances in the electron transfer cross section, which originate from the coupling between high energy channel and low energy channel. In addition, we calculate the electron transfer rates of proton-impact boron atom at different temperatures, which can provide important atomic parameter which support for simulating and diagnosing complex plasma environments.

An ab initio study on the electronic excited states and photodissociation mechanism of bromocarbene molecule.

We used the internally contracted explicitly correlated multireference configuration interaction (icMRCI-F12) method combined with Davidson correction to conduct a high-precision ab initio study of CHBr. The spin-orbit coupling (SOC) is incorporated into the calculation. The 21 spin-free states split into 53 spin-coupled states of CHBr. The vertical transition energies and oscillator strengths are obtained of these states. The SOC effect on the equilibrium structures and the harmonic vibrational frequencies of the ground state X1A', the lowest triplet state a3A'' and the first excited singlet state A1A'' is investigated. The results reveal a significant effect of the SOC on the bond angle and the frequency of the bending mode of a3A''. The potential energy curves of electronic states of CHBr as functions of the H-C-Br bond angle, C-H bond length, and C-Br bond length, respectively, are also investigated. Based on the calculated results, the interactions between electronic states and photodissociation mechanism involved in CHBr in the ultraviolet region are explored. Our theoretical studies will shed light on the complicated interactions and dynamics of the electronic states of bromocarbenes.

The Li + CaF → Ca + LiF chemical reaction under cold conditions.

The calcium monofluoride (CaF) molecule has emerged as a promising candidate for precision measurements, quantum simulation, and ultracold chemistry experiments. Inelastic and reactive collisions of laser cooled CaF molecules in optical tweezers have recently been reported and collisions of cold Li atoms with CaF are of current experimental interest. In this paper, we report ab initio electronic structure and full-dimensional quantum dynamical calculations of the Li + CaF → LiF + Ca chemical reaction. The electronic structure calculations are performed using the internally contracted multi-reference configuration-interaction method with Davidson correction (MRCI + Q). An analytic fit of the interaction energies is obtained using a many-body expansion method. A coupled-channel quantum reactive scattering approach implemented in hyperspherical coordinates is adopted for the scattering calculations under cold conditions. Results show that the Li + CaF reaction populates several low-lying vibrational levels and many rotational levels of the product LiF molecule and that the reaction is inefficient in the 1-100 mK regime allowing sympathetic cooling of CaF by collisions with cold Li atoms.

The spectroscopic and transition properties of ZnHe: MRCI+Q study including spin-orbit coupling

A high level ab initio study on electronic states of ZnHe is carried out by utilizing multireference configuration interaction plus Davidson correction (MRCI+Q) method. The potential energy curves (PECs) of the 9 Λ-S states and the 18 Ω states generated from the Λ-S states after considering the spin-orbit coupling (SOC) effects are computed. Based on the computed potential energy curves, the spectroscopic constants of the bound states of ZnHe are acquired, which are in accordance with the previous theoretical results. The transition properties including dipole moments (DMs) of the Λ-S states, transition dipole moments (TDMs), the vibrational band origins, rotational constants, Franck-Condon factors (FCFs) and the radiative lifetimes of some low-lying states have also been acquired. Comparisons with the available previous works are made. This work give a comprehensive picture of PECs and transition properties for transitions between low-lying excited states and ground state, such as A3Π0+-X1Σ+0+ and C1Π1-X1Σ+0+, and should enhance our understanding on the electronic structure and spectroscopy of ZnHe molecule.

Intersystem crossing and intramolecular triplet excitation energy transfer in spiro[9,10-dihydro-9-oxoanthracene-10,2′-5′,6′-benzindan] investigated by DFT/MRCI methods

Recent experimental studies of a spiro-linked anthracenone (A)–naphthalene (N) compound (AN) in butyronitrile (BuCN) solution (Dobkowski et al., J. Phys. Chem. A 2019, 123, 6978) proposed an excited-state energy dissipation pathway [1ππ* (N) + 1ππ*(A)]↝1 nπ* (A)↝3 nπ* (A)↝3ππ*(N). However, a detailed theoretical study employing combined density functional theory and multireference configuration interaction methods, performed in the present work, suggests that the photoexcitation decay follows a different pathway. In BuCN solution, the intersystem crossing (ISC) follows the well-established El-Sayed rule and involves the 3ππ*(A) state which is found to be the lowest excited triplet state localized on the anthracenone moiety. Because the Dexter triplet excitation energy transfer (TEET) to the first excited triplet state of the naphthalene subunit is forbidden in C2 v symmetry, it is mandatory to go beyond the Condon approximation in modeling this process. Nonadiabatic coupling matrix elements were computed to obtain a TEET rate different from zero. Our calculations yield time constants of 5 ps for the 1 nπ* (A)↝3ππ* (A) ISC and of 3 ps for the subsequent 3ππ* (A)↝3ππ* (N) TEET in BuCN whereas the energy dissipation involving the 3 nπ*(A) state as an intermediate occurs on a much longer time scale.

Extensive theoretical studies of the highly excited electronic states with the experimental parameters calculation for the laser cooling of CaI molecule

By using the multireference configuration interaction method followed by Davidson correction, the electronic structure of the molecule CaI has been investigated. The potential energy curves, the permanent and transition dipole moment curves, and the spectroscopic parameters of 18 electronic states are investigated for these states, along with 111 vibrational levels of the four lowest electronic states. The Franck–Condon factors and the radiative lifetime are calculated for the X2Σ+–(1)2Π transition. For this transition, the vibrational branching ratio, the slowing distance L, and the number of cycles ( N) for photon absorption/emission are calculated along with the Doppler and the recoil temperatures. A pre-cooling temperature in a helium buffer gas is studied and a laser cooling scheme is presented. The calculation of these different experimental parameters is crucial to exploring the optimal conditions under which the laser cooling experiment of CaI molecule will be performed.

Finding Design Principles of OLED Emitters through Theoretical Investigations of Zn(II) Carbene Complexes.

In this work, Zn(II) carbene complexes carrying a dianionic 1,2-dithiolbenzene (dtb) or 1,2-diolbenzene (dob) ligand were investigated regarding their suitability as organic light-emitting diode (OLED) emitter. For the optimization of the complexes, density functional-based methods were used and frequency analyses verified the obtained structures as minima. All calculations were carried out including a polarizable continuum model to mimic solvent-solute interactions. Multireference configuration interaction methods were used to determine excitation energies, spin-orbit couplings, and luminescence properties. Rate constants of spin-allowed and spin-forbidden transitions were calculated according to a Fermi golden rule expression. Using carbene ligands with varying σ-donor and π-acceptor strengths, the luminescence is found to be tunable from yellow to orange/red to deep red/near-infrared. The calculated intersystem crossing (ISC) time constants indicate thermally activated delayed fluorescence (TADF) to be the main decay channel. In contrast to many d10 coinage metal complexes, a parallel orientation of dtb or dob and the carbene ligand is found to be highly favorable. For the complexes with a cyclic (alkyl)(amino) carbene (CAAC) or cyclic (amino)(aryl) carbene (CAArC) ligand, the S1 and T1 states have ligand-to-ligand charge-transfer (LLCT) character and are energetically close. The complex with a classical N-heterocyclic carbene (NHC) ligand has S1 and T1 states with mixed ligand-to-metal charge-transfer (LMCT)/LLCT character and is a very rare example in which the zinc ion contributes to the excitation.

Spectroscopic constants and transition properties of the SnH+ ion excited states including spin-orbit coupling

A high-level ab initio calculation on the electronic states of SnH+ is carried out using multi-reference configuration interaction method (MRCI) in combination with Davidson correction (+Q) and spin-orbit coupling (SOC) effects. The potential energy curves (PECs) of the 21 Λ-S states correlated with six dissociation limits, as well as those of the lowest 31 Ω states generated from the Λ-S states under the SOC effect account are presented. Especially, the states correlated with charge-exchange atomic limit are included in this work. The spectroscopic constants of the bound states are determined, which are in accordance with the available theoretical and experimental results. The transition dipole moments distance dependence, Franck-Condon factors and the radiative lifetimes of the selected transitions are calculated and discussed. In particular, the A1Π1 - a3Π0±,1,2 and 1(Ⅲ) - X1Σ+0+ vibronic bands are predicted. This study is expected to be useful for further interpretation of the detailed electronic spectra of the SnH+ species, as well as complicated rovibronic bands of the other group-IV monohydride cations.

An analytic global potential energy surface of the CsH2 system and the dynamic calculations of the H + CsH reaction

ABSTRACT Based on 17,326 ab initio points, a global potential energy surface (PES) of the ground state of the CsH2 system was constructed using the neural network method. In ab initio calculations, the AVQZ basis set was used for the H atom, the def2-QZVP basis set was adopted for the Cs atom, and a multi-reference configuration interaction method was employed. The topographical characteristics of the newly developed PES were discussed in detail and no wells or barriers were detected. In addition, the dynamical calculations of the H + CsH reaction were performed using the time-dependent wave packet method, based on the new PES. Dynamics properties, such as reaction probability, integral cross section and differential cross-section were examined. The differential cross-section results indicated that the forward abstraction mechanism dominated the abstraction channel, and the ‘rebound' reaction mechanism played a primary role in the exchange channel. Highlights Using the PIP-NN method, A global potential energy surface for the ground state of the CsH2 system was built based on 17,326 ab initio points. Dynamic calculations for the abstraction and exchange channels of the H + CsH reaction were performed using the time-dependent wave packet method and the dynamic properties of these two channels were discussed in detail. The direct abstraction mechanism plays a dominant role in the abstraction channel and the ‘rebound' mechanism dominates the exchange channel.

Ab initio study of the low-lying states of PS molecule

Quantum chemical calculations on the low-lying electronic states of PS correlating with the lowest four dissociation limits are performed by utilizing the internally contracted multireference configuration interaction method (icMRCI) with all-electron Gaussian basis sets. The potential energy curves (PECs) and spectroscopic constants of low-lying bound states are computed. It is of interest to compare the spectroscopic constants of low-lying bound states for the PS molecule with experimental and theoretical results. The detailed information on the properties of the emission 22Π1/2-X12Π1/2, 22Π3/2-X22Π3/2, 12Σ−1/2-X12Π3/2 and 12Σ−1/2-X12Π1/2 bands of PS system, including the transition dipole moments (TDMs), permanent dipole moments (PDMs), Franck-Condon factors (FCFs) and radiative lifetimes, has been identified. We first calculated the f value and radiative lifetime of this radical. Whether the C state is 12Σ− or 12Δ is discussed. According to the calculation results, it is confirmed that the experimental C state is redistributed to 12Δ. Our study should be valuable for further experimental works understanding the spectroscopy and dynamics of the electronic excited states for PS.

The d-d transitions and ligand field parameters for Cr3+/Co2+ doped (Mg, Zn)Al2O4: Multi-reference Ab initio investigations

The normal spinels (Mg, Zn)Al2O4 doped with transition metal (TM) ions Cr3+/Co2+ are versatile materials with important electronic, optical and spectral properties. In addition to being used in many applications, they are excellent systems for testing some models and simulation features. The aim of this paper is to present, in the unified frame, the results on d-d transitions and ligand field parameters (LFPs) for the title systems, based on ab initio calculations, combining periodic density functional theory (DFT) supercell approach with ab initio (AI) multi -reference perturbation theory (MRPT) and multi-reference configuration interaction (MRCI) methods. These AI methods, based on complete active space self-consistent-field (CASSCF) reference, allow to calculate and investigate the energy levels of TM ions and the d-d transitions between them. From the AI results the B and C Racah parameters, the spin-orbit coupling (SOC) constant and the LFPs in the frame of the angular overlap model (AOM) were accurately extracted with ab initio ligand field theory (AILFT) protocol, all with subsequent comparison with the experimental data or existing theoretical results in the literature. The calculation technique presented in this paper serves as a predictive formalism for further studies of larger monomer clusters, for which experimental data is unreliable or unavailable.

A theoretical study on the electronically excited-state spectroscopic properties of phosphorus nitride

ABSTRACT The potential energy curves of 103 Ω states generated from the 39 Λ–S states of PN have been calculated using the internally contracted multireference configuration interaction method with the Davidson modification. Core-valence correlation and scalar relativistic corrections, as well as the basis-set extrapolation to the complete basis set limit are considered. The spin–orbit coupling is computed using the state interaction approach with the Breit-Pauli Hamiltonian. The spectroscopic parameters and molecular constants of bound and quasibound Λ–S and Ω states are evaluated. Our calculated spectroscopic results agree quite well with the available experimental data. The interactions among different electronic states in curve crossing regions have been discussed with the help of computed spin–orbit coupling matrix elements. The perturbations and predissociation phenomena of the A1 , b3 , D1Δ, E1Σ+, and 21 states and so on have been revealed.

Gaseous transport properties of the ground and excited Cr, Co, and Ni cations in He: Ab initio study of electronic state chromatography.

The electronic state chromatography (ESC) effect allows the differentiation of ions in their ground and metastable states by their gaseous mobilities in the limit of low electrostatic fields. It is investigated here by means of accurate transport calculations with ab initio ion-atom potentials for the Cr, Co, and Ni cations in He buffer gas near room temperature. The values for the open-shell ions in degenerate states are shown to be well approximated by using the single isotropic interaction potential. Minimalistic implementation of the multireference configuration interaction (MRCI) method is enough to describe the zero-field transport properties of metastable ions in the 3dm-14s configuration, such as Cr+(a6D), Co+(a5F), and Ni+(4F), due to their weak and almost isotropic interaction with He atom and the low sensitivity of the measured mobilities to the potential well region. By contrast, interactions involving the ions in the ground 3dm states, such as Cr+(a6S), Co+(a3F), and Ni+(2D), are strong and anisotropic; the MRCI potentials poorly describe their transport coefficients. Even the coupled cluster with singles, doubles, and non-iterative triples approach taking into account vectorial spin-orbit coupling may not be accurate enough, as shown here for Ni+(2D). The sensitivity of ion mobility and the ESC effect to interaction potentials, similarities in ion-He interactions of the studied ions in distinct configurations, accuracy and possible improvements of the ab initio schemes, and control of the ESC effect by macroscopic parameters are discussed. Extensive sets of improved interaction potentials and transport data are generated.