Multireference Single - And Double-excitation Configuration Interaction Research Articles

Molecular Opacity Calculations for Lithium Hydride at Low TemperatureSupported by the National Key Research and Development Program of China (Grant No. 2017YFA0402300), the National Natural Science Foundation of China (Grant Nos. 11934004 and 11604052), and the University Nursing Program for Young Scholars with Creative Talents in Heilongjiang Province, China (Grant No. 135409230).

The opacities of the lithium hydride molecule are calculated for temperatures of 300 K, 1000 K, 1500 K, and 2000 K, at a pressure of 10 atm, in which the contributions from the five low-lying electronic states are considered. The ab initio multi-reference single and double excitation configuration interaction (MRDCI) method is applied to compute the potential energy curves (PECs) of the 7LiH, including four 1 Σ + states and one 1 Π state, as well as the corresponding transition dipole moments between these states. The ro-vibrational energy levels are calculated based on the PECs obtained, together with the spectroscopic constants. In addition, the partition functions are also computed, and are provided at temperatures ranging from 10 K to 2000 K for 7LiH, 7LiD, 6LiH, and 6LiD.

Electron capture in slow collisions of O6+ions with atomic hydrogen

Aims. Electron capture in collisions of highly charged O6+ions with ground-state hydrogen atoms is a very important process in solar wind X-ray studies.Methods. In the present study, the full quantum-mechanical molecular-orbital close-coupling method is employed to study electron capture reactions in collisions of O6+ion with ground-state atomic hydrogen in the energy region from 10−4keV u−1to 5 keV u−1. The ab initio multi-reference single- and double-excitation configuration interaction (MRD-CI) method is used to calculate the potential and coupling data used in the QMOCC calculations.Results. Total and state-selective cross sections for the dominant and subdominant reaction channels are calculated and compared with the available experimental and theoretical data. The branching ratios for Lithium-like O5+excited ions are used to calculate the contribution of cascade radiative transitions fromn = 5 levels to the population of 4l states. From the calculated cross sections, reaction rate coefficients are obtained for temperatures between 1000 and 1 × 109K and compared with other calculations.

Molecular opacities of the transitions for the lowest four singlet states of BeH+

The rovibrational transition lines are computed for the lowest four singlet states of BeH+, including three 1Σ+ and one 1Π states, and the collisionally-broadened BeH+ opacities relevant to stellar atmospheres are computed using these line lists for the temperatures of 1800 K, 4500 K, 10,000 K, 20,000 K and a pressure of 100 atms. The ab initio multi-reference single- and double-excitation configuration interaction (MRDCI) method is employed to calculate the potentials and dipole transition momentum, based on which the spectroscopic constants are extracted and the corresponding ro-vibrational energies, Einstein coefficients as well as oscillator strengths are computed with high precision. For the convenience of relevant application, the partition functions are calculated from 100 K to 40,000 K, which are important for the modeling of features of interstellar observations as well as the fusion plasma emissions in the edge and divertor region.

Theoretical investigations of collisions between highly charged ions and atomic H and He

In the present work, the quantum-mechanical molecular-orbital close-coupling (QMOCC) method and the atomic-orbital close-coupling (AOCC) method have been applied to investigate Solar Wind ions (Neq+ Oq+ Nq+ Cq+) colliding with neutral H and He. The multi-reference single- and double-excitation configuration interaction (MRDCI) approach has been applied to compute the adiabatic potential and nonadiabatic couplings, and important configurations have been selected to obtain potentials of very high excited states. Total and state-selective cross sections have been calculated for a large energy range and compared to available experimental and theoretical data.

Ab initio MRSDCI study on the low-lying electronic states of the lithium chloride molecule (LiCl)

Potential energy curves (PECs) for the low-lying states of the lithium chloride molecule (LiCl) have been calculated using the internally contracted multireference single- and double-excitation configuration interaction (MRSDCI) method with the aug-cc-PVnZ (AVnZ) and aug-cc-PCVnZ (ACVnZ) basis sets, where n = T, Q, and 5. First, we calculate PECs for 7 spin-orbit (SO)-free Λ-S states, X(1)Σ(+), A(1)Σ(+), (3)Σ(+), (1)Π, and (3)Π, and then obtain PECs for 13 SO Ω states, X0(+), A0(+), B0(+), 0(-)(I), 0(-)(II), 1(I), 1(II), 1(III), and 2, by diagonalizing the matrix of the electronic Hamiltonian plus the Breit-Pauli SO Hamiltonian. The MRSDCI calculations not including core orbital correlation through the single and double excitations are also performed with the AV5Z and ACV5Z basis sets. The Davidson corrections (Q0) are added to both the Λ-S and Ω state energies. Vibrational eigenstates for the obtained X(1)Σ(+) and X0(+) PECs are calculated by solving the time-independent Schrödinger equation with the grid method. Thus, the effects of basis set, core orbital correlation, and the Davidson correction on the X(1)Σ(+) and X0(+) PECs of LiCl are investigated by comparing the spectroscopic constants calculated from the PECs with one another and with experiment. It is confirmed that to accurately predict the spectroscopic constants we need to include core-electron correlation in the CI expansion and use the basis sets designed to describe core-valence correlation, i.e., ACVnZ. The SO PECs presented in this paper will be of help in the future study of diatomic alkali halide dynamics.

Ab initio calculation of the low-lying electronic states of the ZrN molecule

An ab initio calculation of the low-lying electronic states of zirconium nitride (ZrN) were performed by using a complete active space self-consistent field with multireference single and double excitation configuration interaction (MRSDCI). The potential energy curves of 21 low-lying electronic states of the ZrN molecule with different spin and spatial symmetries, in the representation 2s+1Λ(+/−) and below 30 000 cm–1, were identified. The harmonic frequency (ωe), the equilibrium internuclear distance (Re), the rotational constants (Be), the electronic energy with respect to the ground state (Te), and the permanent dipole moment (µ) were calculated for the considered electronic states. The comparison of these values with those available in the literature shows a very good agreement with either theoretical or experimental data. Fifteen new electronic states were studied here for the first time.

Accurate Bond Energies of Hydrocarbons from Complete Basis Set Extrapolated Multi‐Reference Singles and Doubles Configuration Interaction

Quantum chemistry has become one of the most reliable tools for characterizing the thermochemical underpinnings of reactions, such as bond dissociation energies (BDEs). The accurate prediction of these particular properties (BDEs) are challenging for ab initio methods based on perturbative corrections or coupled cluster expansions of the single-determinant Hartree-Fock wave function: the processes of bond breaking and forming are inherently multi-configurational and require an accurate description of non-dynamical electron correlation. To this end, we present a systematic ab initio approach for computing BDEs that is based on three components: 1) multi-reference single and double excitation configuration interaction (MRSDCI) for the electronic energies; 2) a two-parameter scheme for extrapolating MRSDCI energies to the complete basis set limit; and 3) DFT-B3LYP calculations of minimum-energy structures and vibrational frequencies to account for zero point energy and thermal corrections. We validated our methodology against a set of reliable experimental BDE values of CC and CH bonds of hydrocarbons. The goal of chemical accuracy is achieved, on average, without applying any empirical corrections to the MRSDCI electronic energies. We then use this composite scheme to make predictions of BDEs in a large number of hydrocarbon molecules for which there are no experimental data, so as to provide needed thermochemical estimates for fuel molecules.

Theoretical investigation of charge transfer between N6+and atomic hydrogen

Charge transfer due to collisions of ground-state N{sup 6+}(1s{sup 2} S) with atomic hydrogen has been investigated theoretically using the quantum-mechanical molecular-orbital close-coupling (QMOCC) method, in which the adiabatic potentials and nonadiabatic couplings were obtained using the multireference single- and double-excitation configuration-interaction (MRDCI) approach. Total, n-, l-, and S-resolved cross sections have been obtained for energies between 10 meV/u and 10 keV/u. The QMOCC results were compared to available experimental and theoretical data as well as to merged-beams measurements and atomic-orbital close-coupling and classical trajectory Monte Carlo calculations. The accuracy of the QMOCC charge-transfer cross sections was found to be sensitive to the accuracy of the adiabatic potentials and couplings. Consequently, we developed a method to optimize the atomic basis sets used in the MRDCI calculations for highly charged ions. Since cross sections, especially those that are state selective, are necessary input for x-ray emission simulation of heliospheric and Martian exospheric spectra arising from solar wind ion-neutral gas collisions, a recommended set of state-selective cross sections, based on our evaluation of the calculations and measurements, is provided.

Configuration interaction calculations of cross sections for proton stopping reactions

Purpose: To illustrate the role of quantum mechanical electronic structure methods in providing accurate predictions of the cross sections for ionization and electron capture processes that occur as a result of proton collisions in the high-eV to low-keV energy region.Methods: Calculations are carried out to compute potential curves and non-adiabatic coupling elements for a variety of collision partners employing the ab initio multireference single- and double-excitation configuration interaction (MRD-CI) method. These results are used as input for the electronic-state close-coupling (ESCC) method in order to compute cross sections for various transitions that occur because of collisions.Results: Emphasis is placed on proton-molecule collisions that play a key role in various medical applications as well as in astrophysics and nano-scale materials manufacturing. Examples discussed include the Na-He pair of atoms of interest in recent astrophysical observations, proton collisions with various hydrocarbons and also with water and oxygen, and key ionic products such as H2O+ and H3O+ .Conclusions: The computed cross sections provide a detailed picture of radiation damage dynamics in Monte Carlo simulations. This information can potentially enhance the efficiency of proton beam focusing and also reduce undesirable side effects on body tissues.

Low-energy charge transfer in collisions of He2+with H in a Debye plasma

Charge transfer in collisions of $\ensuremath{\alpha}$ particles with ground-state H embedded in a Debye plasma is studied in the low-energy region from $10$${}^{\ensuremath{-}4}$ eV to $5$ keV. The screened Coulomb interaction is described by the Debye-H\"uckel potential. The relevant molecular potentials and coupling matrix elements are obtained using a modified multireference single-and double-excitation configuration interaction package. Total and state-selective cross sections in the nonradiative charge-transfer collisions from $60$ eV to $5$ keV are calculated using the quantum-mechanical molecular-orbital close-coupling method. Both optical-potential and semiclassical methods have been used in the investigation of the radiative charge transfer from $10$${}^{\ensuremath{-}4}$ to $1$ eV and $1$ to $10$${}^{2}$ eV, respectively. The total cross sections for the no-screening case are in good agreement with the existing data. The effects of the screened Coulomb potential on the electron-capture cross sections are discussed.

Ab initio calculation of the electronic structures of the ∑7+ ground and A Π7 and a ∑5+ excited states of MnH

Electronic structures and molecular constants of the ground (7)Sigma(+) and low-lying A (7)Pi and a (5)Sigma(+) electronic excited states of the MnH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI) with Davidson's correction (+Q) calculations under exact C(infinity v) symmetry using Slater-type basis sets. To correctly describe the (7)Sigma(+) electronic ground state, X (7)Sigma(+), at the MR-SDCI+Q calculation, we employed a large number of reference configurations in terms of the state-averaged complete active space self-consistent field (CASSCF) orbitals, taking into account the contribution from the B (7)Sigma(+) excited state. The A (7)Pi and a (5)Sigma(+) states can well be described by the MR-SDCI wave functions based on the CASSCF orbitals obtained for the lowest state only. In the MR-SDCI+Q, calculations of the X (7)Sigma(+), A (7)Pi, and a (5)Sigma(+) states required 16, 7, and 17 reference configurations, respectively. Molecular constants, i.e., r(e) and omega(e) of these states and excitation energy from the X (7)Sigma(+) state, obtained at the MR-SDCI+Q level, showed a good agreement with experimental values. The small remaining differences may be accounted for by taking relativistic effects into account.

Configuration interaction calculations of annihilation rates for positronic complexes of alkali hydrides

Ab initio multireference single- and double-excitation configuration interaction (MRD-CI) wave functions have been employed to compute the annihilation rates (AR) of positronic molecular complexes of four alkali hydrides. The first step in these calculations is the evaluation of integrals of the two-particle Dirac delta function δ +− over pairs of electronic and positronic basis functions. MRD-CI wave functions calculated with the same basis are then employed to obtain expectation values of the δ +− operator ( Z eff), which in turn are proportional to the corresponding annihilation rates (AR) of the associated many-particle states. The importance of removing near-linear dependencies in the basis sets employed is stressed as well as the advisability of placing diffuse (small-exponent) functions in the basis only at the most electronegative center of the molecule. A tendency to underestimate the Z eff values is noted because of the impracticality of including sufficiently high-l basis functions in the basis for general molecular systems. However, comparison with the relatively accurate values for the four-electron e +LiH complex obtained by Quantum Monte-Carlo (QMC) and other methods indicates that the fractional error is nearly constant over a large range of internuclear distance, consistent with the expectation that missing correlation effects in the MRD-CI treatment are predominantly atomic in nature. A scaling procedure based on the asymptotic δ +− value, which is the same for all four alkali hydrides, is then shown to produce good agreement with the QMC AR data for e +LiH. The same procedure has been applied to the δ +− values for the positronic complexes of the heavier alkali hydrides for which no other theoretical results are available. Trends in the variation of the AR results with bond distance are discussed.

Optimizing Conical Intersections without Derivative Coupling Vectors: Application to Multistate Multireference Second-Order Perturbation Theory (MS-CASPT2)

We introduce a new method for optimizing minimal energy conical intersections (MECIs), based on a sequential penalty constrained optimization in conjunction with a smoothing function. The method is applied to optimize MECI geometries using the multistate formulation of second-order multireference perturbation theory (MS-CASPT2). Resulting geometries and energetics for conjugated molecules including ethylene, butadiene, stilbene, and the green fluorescent protein chromophore are compared with state-averaged complete active space self-consistent field (SA-CASSCF) and, where possible, benchmark multireference single- and double-excitation configuration interaction (MRSDCI) optimizations. Finally, we introduce the idea of "minimal distance conical intersections", which are points on the intersection seam that lie closest to some specified geometry such as the Franck-Condon point or a local minimum on the excited state.

Configuration interaction calculations of positron binding to molecular oxides and hydrides and its effect on spectroscopic constants

Ab initio multireference single- and double-excitation configuration interaction (MRD-CI) calculations have been carried out for magnesium oxide (MgO) and lithium oxide (LiO) and their positronic complexes. These results are compared with previous theoretical data obtained earlier for beryllium oxide (BeO) and the series of alkali hydrides with and without an additional positron. Potential curves have been constructed for each of the systems, MgO, e+MgO, LiO and e+LiO. Positron affinities (PAs) of 0.472eV and 0.304eV, respectively, have been computed for the ground states of MgO and LiO. Because of the relatively low ionization potential of the Li atom, it is found that the dissociation limit in the latter case is Li++PsO (Oe+e−), whereas it is Mg+e+O in the former case, in close analogy to what has been found for e+BeO. Significant changes in bond lengths, vibrational frequencies and dissociation energies are indicated as a result of binding a positron to each of these oxides as well as to the alkali hydrides studied earlier. The general trend observed is toward increased bond length and decreased frequency as a result of attaching a positron to these systems in their various low-lying electronic states.

Ab initio molecular orbital study of ground and low-lying electronic states of CoCN

The ground and low-lying excited states of CoCN have been studied by ab initio multireference single and double excitation configuration interaction (MR-SDCI) calculations with Davidson's correction Q and Cowan-Griffin's relativistic corrections. The electronic ground state of CoCN is (3)Phi(i) and the equilibrium geometry is linear with bond lengths of r(e)(Co-C)=1.8540 A and r(e)(C-N)=1.1677 A, substantially different from the experimentally derived values of r(0)(Co-C)=1.8827(7) A and r(0)(C-N)=1.1313(10) A. The first excited state is (3)Delta(i), separated from the ground state by 727 cm(-1). Larger dynamical electron correlation energy for the low-spin (3)Phi state than for the high-spin (5)Phi state makes the (3)Phi state to be the ground state, which is discussed in terms of the differences in natural orbitals. A new spin-orbit interaction scheme between the X (3)Phi(i) and 1 (3)Delta(i) states is proposed.

Spectroscopic constants and potential energy curves of yttrium carbide (YC)

The potential energy curves of the low-lying electronic states of yttrium carbide (YC) and its cation are calculated at the complete active space self-consistent field and the multireference single and double excitation configuration interaction (MRSDCI) levels of theory. Fifteen low-lying electronic states of YC with different spin and spatial symmetries were identified. The X (4)Sigma- state prevails as the ground state of YC, and a low-lying excited A (4)Pi state is found to be 1661 cm(-1) higher at the MRSDCI level. The computations of the authors support the assignment of the observed spectra to a B (4)Delta(Omega=72)<--A (4)Pi(Omega=52) transition with a reinterpretation that the A (4)Pi state is appreciably populated under the experimental conditions as it is less than 2000 cm(-1) of the X (4)Sigma- ground state, and the previously suggested (4)Pi ground state is reassigned to the first low-lying excited state of YC. The potential energy curves of YC+ confirm a previous prediction by Seivers et al. [J. Chem. Phys. 105, 6322 (1996)] that the ground state of YC+ is formed through a second pathway at higher energies. The calculated ionization energy of YC is 6.00 eV, while the adiabatic electron affinity is 0.95 eV at the MRSDCI level. The computed ionization energy of YC and dissociation energy of YC+ confirm the revised experimental estimates provided by Seivers et al. although direct experimental measurements yielded results with greater errors due to uncertainty in collisional cross sections for YC+ formation.

A theoretical study of TeOH in its electronic ground state

The ab initio multireference single- and double-excitation configuration interaction (MRD-CI) method has been used to calculate the potential surfaces for the six lowest-lying electronic states of the TeOH molecule. The 2 A″ ground state is predicted to have a bent equilibrium geometry. The first excited state, 2 A′, is calculated to lie 2695 cm −1 above the ground state. The MORBID program package has been used for the rotation–vibration analysis of the electronic ground state, for which the term values of the fundamental levels are calculated as 582 cm −1 for the Te–O stretching mode, 959 cm −1 for the bending mode, and 3655 cm −1 for the O–H stretching mode.

Insight into the Rydberg states of CH

Ab initio electronic structure calculations of a relatively large number of Rydberg states of the CH radical were carried out employing the multireference single and double excitation configuration interaction (MRD-CI) method. A Gaussian basis set of cc-pV5Z quality augmented with 12 diffuse functions was used together with an extensive treatment of electron correlation. The main focus of this contribution is to investigate the 3d Rydberg complex assigned by Watson [Astrophys. J. 555, 472 (2001)] to three unidentified interstellar bands. The authors' calculations reproduce quite well the absolute excitation energies of the three components of the 3d complex, i.e., 2Sigma+(3dsigma), 2Pi(3dpi), and 2Delta(3ddelta), but not the energy ordering inferred from a rotational assignment of the 3d<--X 2Pi laboratory spectrum. The computation of the 4d complex is reported for the first time along with a number of other higher lying Rydberg species with an X 1Sigma+ core. The lowest Rydberg states belonging to series converging to the a 3Pi and A 1Pi excited states of CH+ are also calculated.

Ab initio calculation of the electronic structures of the Φ3 ground and Φ5 excited states of CoH

The electronic structures and the spectroscopic constants of the electronic ground Φ3 and low-lying Φ5 electronic excited states of the CoH molecule were studied by multireference single and double excitation configuration interaction (MR-SDCI)+Davidson’s correction (Q) calculations and size-consistent multireference coupled pair approximation (MRCPA) calculations. Calculations were performed under C∞v symmetry using Slater-type basis functions. The electronic ground state was confirmed to be the Φ3 state. It was found that at least four reference configurations were needed to describe the ground Φ3 state correctly at the MR-SDCI+Q level, while the Φ5 state can be described well by one reference configuration, namely, the Hartree-Fock configuration. Larger dynamical electron correlation for the low-spin Φ3 state than that for the high-spin Φ5 state is discussed. Spectroscopic constants, i.e., equilibrium bond lengths (re), harmonic frequency (ωe), and excitation energy, obtained by the MR-SDCI+Q method showed good correspondence with experimental values. MRCPA calculations gave a slightly shorter value for re than experimental values, but improved ωe and the excitation energy bringing them very close to experimental values.

Radiative charge transfer in Ne2+ + He collisions

The optical potential and semiclassical methods have been applied to the studies of radiative charge transfer in collisions of ground-state and metastable Ne2+ ions with neutral helium. Cross sections are presented with relative collision energies between 0.1 meV and 10 keV. For all transitions concerned, the cross sections display rich resonance structures in the low-energy region. From the calculated cross sections, rate coefficients are obtained with temperatures between 10 and 20 × 106 K and are found to be in agreement with available experimental data. The multireference single- and double-excitation configuration-interaction (MRD-CI) method was used to obtain the relevant adiabatic molecular potentials and dipole transition matrix elements.