Large Configuration Interaction Research Articles

Accurate ab initio calculations of adiabatic energy and dipole moment: Prospects for the formation of cold Alkaline-Earth-Francium molecular ions ALKE-Fr+ (ALKE = Be, Mg, Ca, and Sr)

Alkaline-earth and alkali-metal mixtures have an electronic structure that is perfect for laser cooling. This makes them highly attractive for trapping and laser cooling experiments, allowing the formation of cold molecules. For this object, potential-energy curves and relevant spectroscopic parameters of the low-lying electronic excited states of 1,3Σ+, 1,3Π, and 1,3Δ symmetries of molecular-ion systems composed of alkaline-earth-ion and Francium alkali-metal-atom: ALKE-Fr+ (ALKE = Be, Mg, Ca and Sr), are determined using advanced theoretical technique in quantum chemistry, including a non-empirical pseudopotential, core-valence correlation, large Gaussian basis sets and Full Configuration Interaction (FCI). In order to obtain a more accurate understanding of the electronic structure of these systems, we also determined transition and permanent dipole moments and vibrational properties. Thereafter, the spontaneous and the black-body stimulated transition rates were determined and were employed to calculate lifetimes for all vibrational states of the ground electronic states 11Σ+ of molecular-ions under consideration. For the first and the second excited states, radiative lifetimes were investigated via the Franck–Condon approximation including bound-bound and bound-free transitions. High diagonal structure and large Franck Condon Factor (FCF) values f 00 = 0.987, f 11 = 0.959 and f 22 = 0.919 were obtained for the 11Π (v′ = 0, 1, 2)→ 11Σ+ (v = 0, 1, 2) transition making the BeFr+ system a good candidate for laser cooling. Furthermore, the current results could be used to investigate elastic scattering properties in cold-ion-atom collisions for the first excited states and may help the experimentalists for possible formation, spectroscopy, and photoassociation of cold ion-atom mixtures.

Energy natural orbital characterization of nonadiabatic electron wavepackets in the densely quasi-degenerate electronic state manifold.

Dynamics and energetic structure of largely fluctuating nonadiabatic electron wavepackets are studied in terms of Energy Natural Orbitals (ENOs) [K. Takatsuka and Y. Arasaki, J. Chem. Phys. 154, 094103 (2021)]. Such huge fluctuating states are sampled from the highly excited states of clusters of 12 boron atoms (B12), which have densely quasi-degenerate electronic excited-state manifold, each adiabatic state of which gets promptly mixed with other states through the frequent and enduring nonadiabatic interactions within the manifold. Yet, the wavepacket states are expected to be of very long lifetimes. This excited-state electronic wavepacket dynamics is extremely interesting but very hard to analyze since they are usually represented in large time-dependent configuration interaction wavefunctions and/or in some other complicated forms. We have found that ENO gives an invariant energy orbital picture to characterize not only the static highly correlated electronic wavefunctions but also those time-dependent electronic wavefunctions. Hence, we first demonstrate how the ENO representation works for some general cases, choosing proton transfer in water dimer and electron-deficient multicenter chemical bonding in diborane in the ground state. We then penetrate with ENO deep into the analysis of the essential nature of nonadiabatic electron wavepacket dynamics in the excited states and show the mechanism of the coexistence of huge electronic fluctuation and rather strong chemical bonds under very random electron flows within the molecule. To quantify the intra-molecular energy flow associated with the huge electronic-state fluctuation, we define and numerically demonstrate what we call the electronic energy flux.

Optimization of Large Determinant Expansions in Quantum Monte Carlo.

We present a new method for the optimization of large configuration interaction (CI) expansions in the quantum Monte Carlo (QMC) framework. The central idea here is to replace the nonorthogonal variational optimization of CI coefficients performed in usual QMC calculations by an orthogonal non-Hermitian optimization thanks to the so-called transcorrelated (TC) framework, the two methods yielding the same results in the limit of a complete basis set. By rewriting the TC equations as an effective self-consistent Hermitian problem, our approach requires the sampling of a single quantity per Slater determinant, leading to minimal memory requirements in the QMC code. Using analytical quantities obtained from both the TC framework and the usual CI-type calculations, we also propose improved estimators which reduce the statistical fluctuations of the sampled quantities by more than an order of magnitude. We demonstrate the efficiency of this method on wave functions containing 105-106 Slater determinants, using effective core potentials or all-electron calculations. In all the cases, a sub-milli-Hartree convergence is reached within only two or three iterations of optimization.

Atmospheric Fate of the CH3SOO Radical from the CH3S + O2 Equilibrium.

The atmospheric oxidation mechanisms of reduced sulfur compounds are of great importance in the biogeochemical sulfur cycle. The CH3S radical represents an important intermediate in these oxidation processes. Under atmospheric conditions, CH3S will predominantly react with O2 to form the peroxy radical CH3SOO. The formed CH3SOO has two competing unimolecular reaction pathways: isomerization to CH3SO2, which further decomposes into CH3 and SO2, or a hydrogen shift followed by HO2 loss, leading to CH2S. Previous theoretical calculations have suggested that CH2S formation should be the dominant pathway, in disagreement with existing experimental results. Our large active space multireference configuration interaction calculations agree with the experimental results that the formation of CH3 and SO2 is the dominant route and the formation of CH2S and HO2 can, at most, be a minor pathway. We support the calculations with new experiments starting from the OH + CH3SH reaction for CH3S formation under low NOx conditions and find a SO2 yield of 0.86 ± 0.18 within our reaction time of 7.9 s. Model simulations of our experiments show that the SO2 yield converges to 0.98. This combined theoretical and experimental study thus furthers the understanding of the general oxidation mechanisms of sulfur compounds in the atmosphere.

Spectroscopic, structural and lifetime calculations of the ground and low-lying excited states of the BeNa+, BeK+, and BeRb+ molecular ions

Based on the ab-initio approach and using the non-empirical pseudo-potential formalism for Be2+, Na+, K+ and Rb+ cores, large Gaussian basis sets and full valence configuration interaction (FCI), alkali-metal atom and the Beryllium ionic pairs are treated as effective two-electron systems. The potential energy curves and their spectroscopic constants for the low-lying excited states of different1,3Σ+, 1,3Πand 1,3Δ symmetries of these molecular ions have been performed. In addition to the vibrational properties, permanent and transition dipole moments functions have been also calculated and analyzed. The lifetimes of the vibrational states of the ground state are calculated taking into account the decay rates of the vibrational states in terms of spontaneous emission, and stimulated emission induced by black body radiation. The radiative lifetimes of the vibrational levels of the first A1Σ+ and second C1Σ+excited states are calculated using both ‘Franck-Condon’ and ‘Sum rule’ approximations. In all studied alkali-metal Beryllium molecular ions the ground states X1∑+ have much longer lifetimes than any excited states with an order of second, while an order of nanosecond is found for the first and second excited states, A1Σ+ and C1Σ+.

Efficient and stochastic multireference perturbation theory for large active spaces within a full configuration interaction quantum Monte Carlo framework.

Full Configuration Interaction Quantum Monte Carlo (FCIQMC) has been effectively applied to very large configuration interaction (CI) problems and was recently adapted for use as an active space solver and combined with orbital optimization. In this work, we detail an approach within FCIQMC to allow for efficient sampling of fully internally contracted multireference perturbation theories within the same stochastic framework. Schemes are described to allow for the close control over the resolution of stochastic sampling of the effective higher-body intermediates within the active space. It is found that while complete active space second-order perturbation theory seems less amenable to a stochastic reformulation, strongly contracted N-Electron Valence second-order Perturbation Theory (NEVPT2) is far more stable, requiring a similar number of walkers to converge the sc-NEVPT2 expectation values as to converge the underlying CI problem. We demonstrate the application of the stochastic approach to the computation of sc-NEVPT2 within a (24, 24) active space in a biologically relevant system and show that small numbers of walkers are sufficient for a faithful sampling of the sc-NEVPT2 energy to chemical accuracy, despite the active space already exceeding the limits of practicality for traditional approaches. This raises prospects of an efficient stochastic solver for multireference chemical problems requiring large active spaces, with an accurate treatment of external orbitals.

Formation of CO+ by radiative association

ABSTRACT We theoretically estimate formation rate coefficients for CO+ through the radiative association of C+(2P) with O(3P). In 1989, Petuchowski et al. claimed radiative association to be the most important route for CO+ formation in SN 1987A. In 1990, Dalgarno, Du and You challenged this claim. Therefore, in this study, we improve previous estimates of the radiative association rate coefficients for forming CO+ from C+(2P) and O(3P). To do this, we perform quantum mechanically based perturbation theory calculations as well as semiclassical calculations, which are combined with Breit–Wigner theory in order to add the effect of shape resonances. We explicitly include four electronic transitions. The required potential energy and transition dipole-moment curves are obtained through large basis set multireference configuration interaction electronic structure calculations. We report cross-sections and from these we obtain rate coefficients in the range of 10 –10 000 K, finding that the CO+ formation rate coefficient is larger than the previous estimate by Dalgarno et al. Still our results support their claim that in SN 1987A, CO is mainly formed through radiative association and not through the charge transfer reaction CO+ + O → CO + O+ as earlier suggested by Petuchowski et al.

The Simplest Possible Approach for Simulating S0- S1 Conical Intersections with DFT/TDDFT: Adding One Doubly Excited Configuration.

A simple combination of density functional theory/time-dependent density functional theory (DFT/TDDFT) and configuration interaction is presented to fix the incorrect topology of the S0- S1 conical intersection (CI) and allow a description of bond making and bond breaking in photoinduced dynamics. The proposed TDDFT-1D method includes one lone optimized doubly excited configuration in addition to the DFT/TDDFT singly excited states within the context of a large configuration interaction Hamiltonian. Results for ethylene and stilbene are provided to demonstrate that this ansatz can yield physically meaningful potential energy surfaces near S0- S1 avoided crossings without changing the vertical excitation energies far from the relevant crossings. We also investigate the famous linear water example to show that the algorithm calculates the correct topology of the S0- S1 CI and yields the correct geometric phase.

Non-relativistic and relativistic investigation of the low lying electronic states of Sr2+Xe, Sr+Xe and SrXe systems

The potential energy curves and permanent and transition dipole moments of the neutral SrXe and the ionic Sr+Xe systems are calculated with an ab initio approach using pseudopotential techniques, core polarization potentials, large Gaussian basis sets and full configuration interaction for two electron calculations. The spectroscopic constants of the ground state and lower excited states are in good agreement with the available experimental and theoretical works. The spin–orbit coupling is also included for the ionic system Sr+Xe and the neutral one SrXe. Its effect is significant on the potential energy curves, dipole moments and energy level spacing. For SrXe, the spin–orbit splitting has been considered for the states (2)3Σ0,1, (1,2)3Π0,1,2 and (1)3Δ0,1,2,3.

Relativistic large scale CI calculations of energies, transition rates and lifetimes in Ca-like ions between Co VIII and Zn XI

Energies, E1, E2 and M1 transition rates and lifetimes are reported for the lowest 134 fine-structure levels of the 3p63d2, 3p63d4s, 3p53d3 and 3p63d4p configurations in all Ca-like ions between Co VIII and Zn XI. The calculations have been performed using the multiconfiguration Dirac–Hartree–Fock (MCDHF) and relativistic configuration interaction (RCI) methods. Important core–valance and core–core electron correlation effects are systematically accounted with large scale configuration interaction expansion. The Breit interaction and leading quantum-electrodynamical (QED) contributions such as the vacuum polarization and self-energy corrections are also included in the RCI calculations. The results are compared with the compiled data from the NIST ASD and other calculations to evaluate the accuracy of the present calculations. Our results have good agreement with previous relativistic many-body perturbation theory (RMBPT) calculations and the data from the NIST ASD, except for Zn XI. Present calculations provide some missing data, especially for Cu X and Zn XI, in the NIST ASD.

Large-Scale Electron Correlation Calculations: Rank-Reduced Full Configuration Interaction.

We present the rank-reduced full configuration interaction (RR-FCI) method, a variational approach for the calculation of extremely large full configuration interaction (FCI) wave functions. In this report, we show that RR-FCI can provide ground state singlet and triplet energies within kcal/mol accuracy of full CI (FCI) with computational effort scaling as the square root of the number of determinants in the CI space (compared to conventional FCI methods which scale linearly with the number of determinants). Fast graphical processing unit (GPU) accelerated projected σ = Hc matrix-vector product formation enables calculations with configuration spaces as large as 30 electrons in 30 orbitals, corresponding to an FCI calculation with over 2.4 × 1016 configurations. We apply this method in the context of complete active space configuration interaction calculations to acenes with 2-5 aromatic rings, comparing absolute energies against FCI when possible and singlet/triplet excitation energies against both density matrix renormalization group (DMRG) and experimental results. The dissociation of molecular nitrogen was also examined using both FCI and RR-FCI. In each case, we found that RR-FCI provides a low cost alternative to FCI, with particular advantages when relative energies are desired.

Radiative rates for E1, E2, M1, and M2 transitions in Ne-like Hf LXIII, Ta LXIV and Re LXVI

Calculations for energy levels, radiative rates and lifetimes have been performed for three Ne-like ions, namely Hf LXIII, Ta LXIV and Re LXVI, for which the general-purpose relativistic atomic structure package (GRASP) has been adopted. Results are presented among the lowest 121 levels of these ions, which belong to the 2s22p6, 2s22p53ℓ, 2s2p63ℓ, 2s22p54ℓ, 2s2p64ℓ, and 2s22p55ℓ configurations, but CI (configuration interaction) has been considered among a much larger number of levels. No measurements for energy levels are available but comparisons have been made with the earlier similar theoretical results. Additionally, calculations have also been performed with the flexible atomic code (FAC) in order to assess the effect of (much) larger CI on energy levels.

Radiative rates for E1, E2, M1, and M2 transitions in F-like ions with [formula omitted

Energy levels, radiative rates and lifetimes are reported for 19 F-like ions with 55≤Z≤73, among 113 levels of the 2s22p5, 2s2p6, 2s22p43ℓ, 2s2p53ℓ, and 2p63ℓ configurations. The general-purpose relativistic atomic structure package (grasp) has been adopted for the calculations, and radiative rates (and other associated parameters, such as oscillator strengths and line strengths) are listed for all E1, E2, M1, and M2 transitions of the ions. Comparisons are made with earlier available theoretical and experimental energies, especially for Ba XLVIII. Nevertheless, calculations have also been performed with the flexible atomic code (fac), and with a much larger configuration interaction with up to 38 089 levels, for further accuracy assessments, particularly for energy levels.

Pushing configuration-interaction to the limit: Towards massively parallel MCSCF calculations.

A new large-scale parallel multiconfigurational self-consistent field (MCSCF) implementation in the open-source NWChem computational chemistry code is presented. The generalized active space approach is used to partition large configuration interaction (CI) vectors and generate a sufficient number of batches that can be distributed to the available cores. Massively parallel CI calculations with large active spaces can be performed. The new parallel MCSCF implementation is tested for the chromium trimer and for an active space of 20 electrons in 20 orbitals, which can now routinely be performed. Unprecedented CI calculations with an active space of 22 electrons in 22 orbitals for the pentacene systems were performed and a single CI iteration calculation with an active space of 24 electrons in 24 orbitals for the chromium tetramer was possible. The chromium tetramer corresponds to a CI expansion of one trillion Slater determinants (914 058 513 424) and is the largest conventional CI calculation attempted up to date.

Collision strengths and effective collision strengths for Ne-like Ge

We have carried out a calculation of 241 levels for Ne-like Ge (Z = 36) to calculate electron impact collision strengths and effective collision strengths belonging to 1s22s22p5nl, 1s22s12p6nl (n = 3, 4, 5, 6; l = s, p, d, f, g, and h) configurations, which have been calculated by the fully relativistic flexible atomic code (FAC). Our calculations, based on the distorted-wave method with large configuration interactions, are included. Collision strengths have been generated over an electron energy range of (10–20 000 eV) and they have been listed at seven representative energies of 65.33, 1714.98, 2944.1, 4868.3, 7564.6, 11 040, and 15 221 eV in this work, and effective collision strengths data have been calculated from these at electron plasma temperatures 650, 850, 1050, 1250, 1450, 1650, and 1850 eV. Our results are compared with those available in the literature. It is found that the resonance effects are important in calculating the effective collision strengths.

Pair Potential with Submillikelvin Uncertainties and Nonadiabatic Treatment of the Halo State of the Helium Dimer.

The pair potential for helium is computed with accuracy improved by an order of magnitude relative to the best previous determination. For the well region, its uncertainties are now below 1millikelvin. The main improvement is due to the use of explicitly correlated wave functions at the nonrelativistic Born-Oppenheimer (BO) level of theory. The diagonal BO and the relativistic corrections are obtained from large full configuration interaction calculations. Nonadiabatic perturbation theory is used to predict the properties of the halo state of the helium dimer. Its binding energy and the average value of the interatomic distance are found to be 138.9(5)neV and 47.13(8)Å. The binding energy agrees with its first experimental determination of 151.9(13.3)neV [Zeller etal., Proc. Natl. Acad. Sci. U.S.A. 113, 14651 (2016)PNASA60027-842410.1073/pnas.1610688113].

Iterative submatrix diagonalisation for large configuration interaction problems

ABSTRACT The Davidson method has been highly successful for solving for eigenpairs of the large matrices that are common in quantum chemical simulations. Electronic structure simulations, however, can still easily generate matrices that are too large for current computational resources to handle. Therefore, many strategies have arisen to obtain eigenpairs of sufficient accuracy without considering the full Hamiltonian matrix. This article introduces one such strategy by creating a systematic series of submatrix approximations to the full matrix using natural orbitals. By solving for eigenpairs in this series, the eigenvalue accuracy can be gradually increased until a convergence threshold is reached. Importantly, this allows the series to terminate without ever reaching the full matrix, resulting in lower computational costs and reduced memory demands. Application of the method to the full configuration interaction problem for ground states, excited states and potential energy scans of various systems shows that the iterative submatrix diagonalisation method can systematically control eigenvalue errors and provide substantial cost-savings. This method is therefore expected to be highly useful for large-scale diagonalisation problems in electronic structure theory.

Combining Multiconfiguration and Perturbation Methods: Perturbative Estimates of Core–Core Electron Correlation Contributions to Excitation Energies in Mg-Like Iron

Large configuration interaction (CI) calculations can be performed if part of the interaction is treated perturbatively. To evaluate the combined CI and perturbative method, we compute excitation energies for the 3 l 3 l ′ , 3 l 4 l ′ and 3 s 5 l states in Mg-like iron. Starting from a CI calculation including valence and core–valence correlation effects, it is found that the perturbative inclusion of core–core electron correlation halves the mean relative differences between calculated and observed excitation energies. The effect of the core–core electron correlation is largest for the more excited states. The final relative differences between calculated and observed excitation energies is 0.023%, which is small enough for the calculated energies to be of direct use in line identifications in astrophysical and laboratory spectra.

Energy levels and radiative rates for transitions in Fe V, Co VI and Ni VII

Energy levels, Landé g-factors and radiative lifetimes are reported for the lowest 182 levels of the 3d4, 3d34s and 3d34p configurations of Fe V, Co VI and Ni VII. Additionally, radiative rates (A-values) have been calculated for the E1, E2 and M1 transitions among these levels. The calculations have been performed in a quasi-relativistic approach (QR) with a very large configuration interaction (CI) wavefunction expansion, which has been found to be necessary for these ions. Our calculated energies for all ions are in excellent agreement with the available measurements, for most levels. Discrepancies among various calculations for the radiative rates of E1 transitions in Fe V are up to a factor of two for stronger transitions (f≥0.1), and larger (over an order of magnitude) for weaker ones. The reasons for these discrepancies have been discussed and mainly are due to the differing amount of CI and methodologies adopted. However, there are no appreciable discrepancies in similar data for M1 and E2 transitions, or the g-factors for the levels of Fe V, the only ion for which comparisons are feasible.

Energy levels and radiative rates for Cr-like Cu VI and Zn VII

Energy levels and radiative rates (A-values) for transitions in Cr-like Cu VI and Zn VII are reported. These data are determined in the quasi-relativistic approach (QR), by employing a very large configuration interaction (CI) expansion which is highly important for these ions. No radiative rates are available in the literature to compare with our results, but our calculated energies are in close agreement with those compiled by NIST and other available theoretical data, for a majority of the levels. The A-values (and resultant lifetimes) are listed for all significantly contributing E1, E2 and M1 radiative transitions among the energetically lowest 322 levels of each ion.