Contracted Multireference Configuration Interaction Research Articles

Electronic Structure of Diatomic Nickel Sulfide.

The nature of the Ni-S bond is investigated due to its role in the absorption of atmospheric Lewis acid gases such as SO2 and SO3 onto Ni surfaces. The vibrational frequency and electronic structure of NiS were predicted using CCSD(T), CASSCF, and internally contracted multireference configuration interaction (icMRCI) + Q. 43 density functional theory (DFT) functionals were benchmarked. CASSCF predicted the ground state of NiS to be the 5Δ state arising from the 3d8(3F)4s2 (3F) and 3d9(2D)4s (3D) electronic configurations of Ni. When dynamical correlation effects are included at the icMRCI + Q level, the ground state of Ni-S is predicted to be 3Σ- consistent with the experiment. The vibrational frequency of Ni-S is calculated to be 519.1 cm-1 at the icMRCI + Q level, in reasonable agreement with the experimental value of 512.68 cm-1. CCSD(T) predicts the frequency of Ni-S to be 543.2 cm-1 when extrapolated to the complete basis set (CBS) limit. The Feller-Peterson-Dixon value based on the CCSD(T)/CBS extrapolation for the bond dissociation energy of NiS is 350.6 kJ/mol, within <4 kJ/mol of experiment. Of the 43 DFT functionals, BP86 and O3LYP predicted the vibrational frequency in closest agreement with the experiment. The applicability of DFT to such acid gas systems was further demonstrated by calculating the energy for displacement of NiO by SO to yield NiS and O2. This displacement energy was calculated to be within experimental error for ∼50% of the DFT functionals, but large differences were also predicted for some functionals.

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.

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 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 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.

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.

An ab initio diabatic study of rovibronic spectra of CN.

An ab initio study of the rovibronic spectra for the cyano radical (CN) based on a diabatic representation is presented. This work considers 17 electronic states, 59 dipole moment curves, 88 spin-orbit coupling curves, and 30 electronic angular momentum coupling curves, which are obtained using the internally contracted multireference configuration interaction method including the Davidson correction (icMRCI + Q) with the aug-cc-pwCV5Z-DK basis set. The diabatic transformations are performed based on a property-based diabatization method to remove the avoided crossings for the D2Π-H2Π and b4Π-24Π pairs. Ab initio potential energy curves of the X2Σ+, B2Σ+, E2Σ+, A2Π, D2Π, H2Π, F2Δ and J2Δ electronic states are shifted to match the experimental electronic excitation energies and the equilibrium internuclear distances. The coupled nuclear motion Schrödinger equations are then solved to obtain the rovibronic spectra of CN for wavenumbers from 0 to 80 000 cm-1. At wavenumbers of 0-30 000 cm-1, our absorption cross sections agree well with available theoretical data. For wavenumbers above 30 000 cm-1, our cross sections are larger than previous data in view of the fact that the transitions involving high-lying electronic states are considered. This work provides an overall prediction of the rovibronic spectrum of CN. Our results are suitable for temperatures below 8000 K and could be useful for the investigations of planetary exploration.

A systematic study on spectroscopic and transition properties of the phosphorus mononitride cation

The potential energy curves (PECs) of 28 Λ–S states of the phosphors mononitride cation have been constructed by using the internally contracted multireference configuration interaction (icMRCI) method plus Davidson correction (+Q). The effect of core correlation and scalar relativistic treatment of electron, and the basis-set extrapolation to the complete basis set limit are considered. The spin–orbit coupling is computed via the full Breit-Pauli Hamiltonian. The transition dipole moments (TDMs) for the dipole-allowed and spin-forbidden transitions are calculated. Utilizing the PECs and TDMs, the spectroscopic and transition properties of bound states are then evaluated. The current spectroscopic parameters, vibrational band origins, Einstein coefficients, and Franck-Condon factors well match the available measured values. And the radiative lifetimes for most excited states are estimated for the first time. These results can be useful in the analysis and assignment of molecular spectra or as guidelines for detecting these states spectroscopically.

Transport cross sections and collision integrals for C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions

Transport collision integrals of interacting atoms or ions play a crucial role in modeling transport properties of high-temperature gases and plasmas. Here, we obtained the potential energy curves (PECs) of CH+ using the internally contracted multireference configuration interaction method with the Davidson correction (icMRCI+Q) method. The PECs were then used to investigate the transport cross sections and transport collision integrals for the C+(2P)–H(2S), C(3P)–H+(1S), C(1D)–H+(1S), and C+(4P)–H(2S) interactions using the classical mechanical approach and a quantum mechanical treatment of the scattering with Wentzel–Kramers–Brillouin approximations of the scattering phase shifts. The transport cross sections were obtained in the collision energy of 10−6–1 hartree, which were used to compute transport collision integrals for C–H+ and C+–H systems over the temperature range of 500–40 000 K. The C(1D)–H+(1S) and C+(4P)–H(2S) interactions are considered for the first time. Our transport collision integrals can provide data references for computing transport properties of high-temperature plasmas involving C and H atoms/ions.

Ab initio investigation on predissociation of the A2Σ+ state of the SeH radical induced by spin-orbit coupling

High-level ab initio calculations are performed to investigate potential energy curves (PECs) of seven low-lying Λ-S states associated with the two lowest dissociation limits of the SeH radical by utilizing the internally contracted multireference configuration interaction (icMRCI) method in combination with the aug-cc-pwCV5Z Gaussian basis set. The scalar relativistic effect (SR), the electronic core-valence (CV) correction, and Davidson (+Q) modification are included in our calculations. The fourteen Ω states generated from the seven Λ-S states are yielded when the spin-orbit coupling (SOC) effect is taken into account by using the Breit-Pauli operator. On the ground of the obtained PECs, the spectroscopic constants of the bound Λ-S and Ω states are evaluated, which reproduce pretty well the available experimental and theoretical values. By virtue of SOC matrix elements between the bound A2Σ+ state and repulsive 4Σ–(I), 2Σ–(I), or 4∏(I) states crossing with the A2Σ+ state PEC, the spin-orbit perturbations in the A2Σ+ rovibrational manifold in the crossing region and the A-state predissociation mechanism are analyzed. It is clearly exhibited that the avoided crossing phenomena between electronic states possessing the same Ω quantum number provide obvious spectroscopic effects in the transition dipole moments (TMDs) and Franck-Condon factors (FCFs) of the A2Σ+-X2Π transition. The radiative lifetimes of the A2Σ+ vibrational sublevels are determined. In addition, we finalized our study of the SeH molecule by optimizing its equilibrium ground state geometry in terms of a restricted coupled cluster approach including singles and doubles with perturbative triples account (RCCSD(T) method) plus CV, SR, and SOC corrections with extrapolating to complete basis set (CBS) limit.

Theoretical Study on the Spectroscopic Properties and Photodissociation Mechanism of Dibromocarbene.

Detailed calculations on the electronic states of dibromocarbene (CBr2) herein are presented. First, the spectroscopic properties of the electronic states including geometry parameters, harmonic vibrational frequencies and transition energies of the lowest electronic states of the neutral radical were calculated in detail using the internally contracted multireference configuration interaction methods including Davidson correction (icMRCI+Q) with correlation consistent basis sets of aug-cc-pVXZ (X = T, Q, 5). Second, as CBr2 including two Br atoms, the Spin-Orbit Coupling (SOC) effect on the spectroscopic parameters and the one-dimensional cuts of the potential energy surface (PESs) of the lowest three states were studied. The barrier to linearity and dissociation of the singlet state were discussed. Third, the one-dimensional cuts along with the vertical transition energy (VTE), the oscillator strength, and so on of the electronic states related to the several lowest dissociation limits of CBr2 were calculated at the icMRCI+Q/aug-cc-pVTZ level. Based on the computed results of the electronic states of the radical, the photodissociation mechanism in the UV region were discussed in detail. The ab initio calculations are compared with the previous theoretical and experimental data and are in good agreement. The present work will provide a comprehensive understanding on the electronic structures and dissociation dynamics for the electronic states of the CBr2 radical.

Reaction dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on a global CHIPR potential energy surface of the ground state Si2C(X 1A1)

ABSTRACT The dynamics of C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) on its ground state Si2C(X 1A1) are of great significance in carbon-rich interstellar chemistry. Using the combined-hyperbolic-inverse-power-representation method, we construct the first global potential energy surface (PES) for the electronic ground state Si2C(X 1A1) based on a total of 4080 ab initio energy points, which are obtained at the Davidson-corrected internally contracted multireference configuration interaction level of theory. The topographical features of the newly constructed PES are examined in detail and show good agreement with previous theoretical and experimental studies. Finally, we investigate the C(3P) + Si2(X $^{3}\Sigma ^-_g$ ) → Si(3P) + SiC(X 3Π) reaction using the quasi-classical trajectory and time-dependent wave packet calculations, yielding reasonable integral cross sections and rate constants, which are expected to be useful for astrochemical modelling in carbon-rich interstellar environments.

Toward an efficient implementation of internally contracted coupled-cluster methods.

A new implementation of the internally contracted multireference coupled-cluster with singles and doubles (icMRCCSD) method is presented. The new code employs an efficient tensor contraction kernel and can also avoid full four-external integral transformations, which significantly extends the scope of the applicability of icMRCCSD. The new implementation is currently restricted to the simple case of two active electrons in two orbitals and also supports the computation of spin-adapted doublet and triplet coupled-cluster wavefunctions. This contribution describes the basic approach for the automated derivation of working equations and benchmarks the current code against efficient implementations of standard methods, such as single-reference coupled-cluster singles and doubles (CCSD) and internally contracted multireference configuration interaction (icMRCI). Run times for linearized variants of icMRCCSD are only twice as long as comparable CCSD runs and similar to those of the icMRCI implementation, while non-linear terms of more complete variants of icMRCCSD lead to an order of magnitude longer computation times. Nevertheless, the new code allows for computations at larger scales than it was possible previously, with less demands on memory and disk-space resources. This is exemplified by numerical structure optimizations and harmonic force field determinations of NC2H5 isomers and the singlet and triplet states of m-benzyne. In addition, the exchange coupling of a dinuclear copper complex is determined. This work also defines a new commutator approximation for icMRCCSD, which includes all terms that are also present in the single-reference CCSD method, thus yielding a consistent pair of single-reference and multireference coupled-cluster methods.

Introducing MPEC: Massively parallel electron correlation.

We have developed a new program for carrying out improved internally contracted Multi-reference Configuration Interaction Singles and Doubles (i2cMRCISD) calculations. It is designed from the ground up to be used on distributed memory parallel computers. Tests show good scaling properties with the number of cores per node and the number nodes. This program features Gaussian basis sets with ℓ > 6; scalar special relativity via the spin-free method; convergence to C∞v, D∞v, or spherical electronic states; special code to determine Rydberg orbitals; both uncontracted and contracted MRCISD wavefunctions; one and two electron properties, including full spin-orbit matrix elements with the Breit interaction; analytic calculation of Born-Oppenheimer diagonal correction for multi-configuration Hartree-Fock wavefunctions; and analytic calculation of second order Born-Oppenheimer corrections for Hartree-Fock wavefunctions. The program can be obtained from software.nasa.gov.

Electronic excited states of monobromosilylene molecules including the spin-orbit-coupling.

We employ the internally contracted multireference configuration interaction (icMRCI-F12) with Davidson corrections to explore the electronic states of monobromosilylene molecules (HSiBr). A total of 20 states with energy up to 8.7 eV and the corresponding 50 states after taking the spin-orbit coupling (SOC) effects into account are investigated. The spectroscopic constants of the low-lying states, as well as oscillator strengths, vertical transition energies and potential energy curves (PECs) for all the 20 spin-free states and the 50 spin-orbit-coupled states of HSiBr are presented. The results indicate that the SOC effect significantly affects the dissociation pathways and the PECs of electronic excited states of HSiBr. Based on our calculation results, the interactions between the states and the dissociation of HSiBr in the UV region are discussed. Our study sheds some light on the complex interactions and dynamics of the electronic excited states of HSiBr, which would provide valuable information for future experimental investigations.

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.

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.

A quantum mechanical calculation of the CN radiative association

ABSTRACT Radiative association of CN is investigated through the quantum mechanical method, including the cross sections and rate coefficients. The ab initio potential energy curves, transition dipole moments, and permanent dipole moments of CN are obtained by the internally contracted multireference configuration interaction method with Davidson correction and aug-cc-pwCV5Z-DK basis set. For the collision of the ground state C (3Pg) and N (4Su) atoms, except for the four previously studied processes including the A2Π → X2Σ+, X2Σ+ → A2Π, A2Π → A2Π, and X2Σ+ → X2Σ+ transitions, four other radiative association processes including b4Π → a4Σ+, a4Σ+ → b4Π, b4Π → b4Π, and a4Σ+ → a4Σ+ transitions are considered. We also considered the collision of the excited C (1Dg) and the ground N (4Su) atoms including the 24Π → 14Σ− process and the collision of the ground C (3Pg) and the excited N (2Du) atoms including 22Π → B2Σ+, 32Π → B2Σ+, and 42Π → B2Σ+ transitions. The temperature population factor is considered to describe the thermal population of the three different dissociation asymptotic energies. The results show that the contribution of the A2Π → X2Σ+ and b4Π → a4Σ+ transitions to the total rate coefficients is significant over the entire temperature range. While considering the collision of C and N involving excited states, the contribution of the 22Π → B2Σ+, 32Π → B2Σ+, and 42Π → B2Σ+ transitions to the total rate coefficients cannot be ignored at the temperature range larger than 10 000 K. Finally, the rate coefficients are fitted to an analytical function for astrochemical reaction modelling.

Adiabatic potential energy surfaces and photodissociation mechanisms for highly excited states of H2O

Full-dimensional adiabatic potential energy surfaces of the electronic ground state X̃ and nine excited states Ã, Ĩ, B̃, C̃, D̃, D̃′, D̃″, Ẽ′ and F̃ of H2O molecule are developed at the level of internally contracted multireference configuration interaction with the Davidson correction. The potential energy surfaces are fitted by using Gaussian process regression combining permutation invariant polynomials. With a large selected active space and extra diffuse basis set to describe these Rydberg states, the calculated vertical excited energies and equilibrium geometries are in good agreement with the previous theoretical and experimental values. Compared with the well-investigated photodissociation of the first three low-lying states, both theoretical and experimental studies on higher states are still limited. In this work, we focus on all the three channels of the highly excited state, which are directly involved in the vacuum ultraviolet photodissociation of water. In particular, some conical intersections of D̃–Ẽ′, Ẽ′-F̃, ÖĨ and Ĩ–C̃ states are clearly illustrated for the first time based on the newly developed potential energy surfaces (PESs). The nonadiabatic dissociation pathways for these excited states are discussed in detail, which may shed light on the photodissociation mechanisms for these highly excited states.