Configuration Interaction Research Articles

An ab initio study of the electronic structure and spectroscopy of CO+ and CS+ diatomic cations

In this study, accurate ab initio methods are used to determine the electronic structure and spectroscopic properties of CS + and CO + cations of astrophysical relevance. The core-valence, scalar relativistic and complete basis set extrapolation (CBS) corrections are used in conjunction with the multireference configuration interaction method to obtain accurate properties. The results obtained are very satisfactory in comparison with the experiment. The potential energy curves have been plotted up to reasonable distances, allowing their asymptotes to be adequately described. The ionisation potentials of the neutral molecules were determined. They are 11.26 eV and 14.02 eV for CS and CO respectively. The vibrational energy levels and the rotational constants are also calculated. Our values are in very good agreement compared with the experiment. For instance, we have G ( 0 ) = 686.550 cm − 1 for the ground state X 2 Σ + ( CS + ), while the experimental value is 686.841 cm − 1 . New data for G ( 0 ) and for the rotational constants of the other states are proposed. The Franck-Condon Factors values computed are in perfect agreement with the experimental ones and this implies an accurate description of the transition properties and the radiative lifetimes.

SDSPT2s:SDSPT2 with Selection.

As an approximation to SDSCI [static-dynamic-static (SDS) configuration interaction (CI), a minimal MRCI; Theor. Chem. Acc. 2014, 133, 1481], SDSPT2 [Mol. Phys. 2017, 115, 2696] is a CI-like multireference (MR) second-order perturbation theory (PT2) that treats single and multiple roots in the same manner. This feature permits the use of configuration selection over a large complete active space (CAS) P to end up with a much reduced reference space P̃, which is connected only with a small portion (Q̃1) of the full first-order interacting space Q connected to P. The most expensive portion of the reduced interacting Q̃1 space (which involves three active orbitals) can further be truncated by partially bypassing its generation followed by an integral-based cutoff. With marginal loss of accuracy, the selection-truncation procedure, along with an efficient evaluation and storage of internal contraction coefficients, renders SDSPT2s (SDSPT2 with selection) applicable to systems that cannot be handled by the parent CAS-based SDSPT2, as demonstrated by several challenging showcases.

The low-lying electronic states of 4H-pyran-4-thione; a photoionization and vacuum ultraviolet absorption study, with interpretation by configuration interaction and density functional calculations for the ionic and singlet states.

Two synchrotron-based studies on 4H-pyran-4-thione, photoelectron spectroscopy and vacuum ultraviolet (VUV) absorption spectra were performed. A highly resolved structure was observed in the photoelectron spectrum (PES), in contrast to an earlier PES study, where little structure was observed. The sequence of ionic states was determined using configuration interaction and coupled cluster methods. The vibrational structure of the lowest three PES bands was analyzed by configuration interaction and density functional calculations, providing a detailed explanation of the observed profiles. Several vibrational bands in the VUV absorption spectrum showed a similar structure to the bands in the PES and were identified as Rydberg states.

Selected configuration interaction for high accuracy and compact wave functions: Propane as a case study.

Traditionally, because of the limit of full configuration interaction, complete active space (CAS) theory is most often used to model bond dissociation and other dynamical processes where the multi-reference character becomes important. Inconveniently, the CAS method is highly dependent on the choice of active space and, therefore, inherently non-black-box, in addition to the exponential scaling with respect to electrons and orbitals. This illustrates the need for methods that can accurately treat multi-reference electronic structure problems without significant dependence on input parameters. Selected configuration interaction (SCI) methods have experienced a revival in recent years because of their independence of these predicaments. SCI methods aim to exploit the sparsity of the full configuration interaction space to identify all relevant electronic configurations and, therefore, keep the wave function as compact as possible while still representing the total multi-reference electronic structure accurately. In this work, we take the recent achievement by Gao et al. to run full configuration interaction on the propane molecule in a minimal basis set (23 electrons in 26 orbitals) as an occasion to demonstrate that our SCI methods implemented in the GeneralSCI program package can achieve high energetic accuracy in conjunction with very compact wave functions, which considerably alleviate computational cost. Furthermore, we show the good performance of our SCI methods in reproducing a propane bond dissociation surface and energy. This illustrates that SCI methods can be readily applied to problems in chemical reactivity.

Kohn-Sham inversion for open-shell systems.

Methods based on density-functional theory usually treat open-shell atoms and molecules within the spin-unrestricted Kohn-Sham (KS) formalism, which breaks symmetries in real and spin space. Symmetry breaking is possible because the KS Hamiltonian operator does not need to exhibit the full symmetry of the physical Hamiltonian operator, but only the symmetry of the spin density, which is generally lower. Symmetry breaking leads to spin contamination and prevents a proper classification of the KS wave function with respect to the symmetries of the physical electron system. Formally well-justified variants of the KS formalism that restore symmetries in real space, in spin space, or in both have been introduced long ago, but have rarely been used in practice. Here, we introduce numerically stable KS inversion methods to construct reference KS potentials from reference spin-densities for all four possibilities to treat open shell systems, non-symmetrized, spin-symmetrized, space-symmetrized, and fully-symmetrized. The reference spin-densities are obtained by full configuration interaction and high-level coupled cluster methods for the considered atoms and diatomic molecules. The decomposition of the total energy in contributions such as the non-interacting kinetic, the exchange, and the correlation energy is different in the four KS formalisms. Reference values for these differences are provided for the considered atoms and molecules. All KS inversions, except the fully symmetrized one, lead in some cases to solutions violating the Aufbau principle. In the purely spin-symmetrized KS formalism, this represents a violation of the KS v-representability condition, i.e., no proper KS wave functions exist in those cases.

Phaseless Auxiliary-Field Quantum Monte Carlo Method for Cavity-QED Matter Systems.

We present a generalization of the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to cavity quantum-electrodynamical (QED) matter systems. The method can be formulated in both the Coulomb and the dipole gauge. We verify its accuracy by benchmarking calculations on a set of small molecules against full configuration interaction and state-of-the-art QED coupled cluster (QED-CCSD) calculations. Our results show that (i) gauge invariance can be achieved within correlation-consistent Gaussian basis sets, (ii) the accuracy of QED-CCSD can be enhanced significantly by adding the standard perturbative triples correction without light-matter coupling, and (iii) there is a straightforward way to evaluate the differential expression for the photon occupation number that works in any gauge. The high accuracy and favorable computational scaling of our AFQMC approach will enable a broad range of applications. Besides polaritonic chemistry, the method opens a way to simulate extended QED matter systems.

A theoretical investigation of spectroscopy properties and transition properties of TlBr+ cation

The potential energy curves, dipole moments and transition dipole moments of the 14 Λ–S states and 30 Ω states of TlBr+ cation were performed using the multi-reference configuration interaction method. The Davidson correction and spin–orbit coupling effects were also considered. The spectroscopic properties and transition properties of TlBr+ cation were reported at the first time. The results show that the X2Π is the ground state and the A2Σ+ is the first excited state, which are both weakly bound states. 14 Λ–S states are all electronically bound except for the 24Π state, which is repulsive. The phenomenon of avoided crossing in the Ω states occurs in the energy region between 30,000 and 50,000 cm−1. The Franck–Condon factors, radiative lifetimes and emission coefficients between the and transitions are both calculated. The results indicated that the radiative lifetimes of the and states are too large to laser cooling TlBr+ cation, laser cooling of TlBr+ cation is not feasible. These results provide a theoretical basis to explore the spectroscopic properties of TlBr+ cation.

Benchmark computations of nearly degenerate singlet and triplet states of N-heterocyclic chromophores. II. Density-based methods.

In this paper, we demonstrate the performance of several density-based methods in predicting the inversion of S1 and T1 states of a few N-heterocyclic triangulene based fused ring molecules (popularly known as INVEST molecules) with an eye to identify a well performing but cost-effective preliminary screening method. Both conventional linear-response time-dependent density functional theory (LR-TDDFT) and ΔSCF methods (namely maximum overlap method, square-gradient minimization method, and restricted open-shell Kohn-Sham) are considered for excited state computations using exchange-correlation (XC) functionals from different rungs of Jacob's ladder. A well-justified systematism is observed in the performance of the functionals when compared against fully internally contracted multireference configuration interaction singles and doubles and/or equation of motion coupled-cluster singles and doubles (EOM-CCSD), with the most important feature being the capture of spin-polarization in the presence of correlation. A set of functionals with the least mean absolute error is proposed for both the approaches, LR-TDDFT and ΔSCF, which can be more cost-effective alternatives for computations on synthesizable larger derivatives of the templates studied here. We have based our findings on extensive studies of three cyclazine-based molecular templates, with additional studies on a set of six related templates. Previous benchmark studies for subsets of the functionals were conducted against the domain-based local pair natural orbital-similarity transformed EOM-CCSD (STEOM-CCSD), which resulted in an inadequate evaluation due to deficiencies in the benchmark theory. The role of exact-exchange, spin-contamination, and spin-polarization in the context of DFT comes to the forefront in our studies and supports the numerical evaluation of XC functionals for these applications. Suitable connections are drawn to two and three state exciton models, which identify the minimal physics governing the interactions in these molecules.

Restoring rotational symmetry of multicomponent wavefunctions with nuclear orbitals.

In this work, we present a non-orthogonal configuration interaction (NOCI) approach to address the rotational corrections in multicomponent quantum chemistry calculations where hydrogen nuclei and electrons are described with orbitals under Hartree-Fock (HF) and density functional theory (DFT) frameworks. The rotational corrections are required in systems such as diatomic (HX) and nonlinear triatomic molecules (HXY), where localized broken-symmetry nuclear orbitals have a lower energy than delocalized orbitals with the correct symmetry. By restoring rotational symmetry with the proposed NOCI approach, we demonstrate significant improvements in proton binding energy predictions at the HF level, with average rotational corrections of 0.46eV for HX and 0.23eV for HXY molecules. For computing rotational excitation energies, our results indicate that HF kinetic energy corrections are consistently accurate, while discrepancies arise in total energy predictions, primarily from an incomplete treatment of dynamical correlation effects. Rotational energy corrections in multicomponent DFT calculations, using the epc17-2 proton-electron correlation functional, lead to an overestimation of proton binding energies. This is as a result of double-counting of proton-electron correlation effects in the off-diagonal NOCI terms. As a correction, we propose a scaling scheme that effectively adjusts the proton-electron correlation contributions, bringing our results into close agreement with reference CCSD(T) data. The scaled rotational corrections, on average, increase the epc17-2 proton binding energy predictions by 0.055eV for HX and 0.025eV for HXY and yield average deviations of 1.0 cm-1 for rotational transitions.

The Properties of the Low-Lying Electronic States and Avoided Crossings of the SbP Molecule: A Theoretical Investigation Includes Spin-Orbit Coupling.

High-level multireference configuration interaction plus Davidson correction (MRCI + Q) calculation method was employed to determine the potential energy curves (PECs) of 10 Λ-S states, which come from the first and second dissociation channels of the SbP molecule, as well as 34 Ω states considering the spin-orbit coupling (SOC) effect. By solving the Schrödinger equation for nuclear motion, spectroscopic constants for the ground state X1Σ+ and low-lying excited states were obtained and compared with experimental data. The excellent agreement indicates the reliability of our calculations. Additionally, the calculated spin-orbit (SO) matrix elements of the 13Π and 15Π states with other Λ-S states were analyzed, and the majority of the values in the Franck-Condon region exceed 200 cm-1, indicating strong interactions between these states. What's more, the joint effects of spin-orbit coupling and avoided crossing were discussed in detail, leading to the complex potential energy curves and double-well phenomena observed in the Ω states. Taking forbidden transitions into account, transition dipole moments with the SOC effect are considered. The Franck-Condon factors, Einstein coefficients, and radiative lifetimes for the 13Σ+1 ↔ X1Σ+0+ transition were obtained. Analysis indicates that direct laser cooling of SbP is inappropriate.

A Theoretical Study on Crossings Among Electronically Excited States and Laser Cooling of Group VIA (S, Se, andTe) Hydrides.

Various electronically excited states and the feasibility of direct laser cooling of SH, SeH, and TeH are investigated using the highly accurate abinitio and dynamical methods. For the detailed calculations of the seven low-lying Λ-S states of SH, we utilized the internally contracted multireference configuration interaction approach, considering the spin-orbit coupling (SOC) effects. Our calculated spectroscopic constants are in very good agreement with the available experimental results. It is found that, from SH to TeH, the crossing points among the A2Σ+ and three electronically excited states gradually shift downward toward the ground vibrational level of the A2Σ+ state. This is consistent with our previous findings in other molecular systems and makes the laser cooling of TeH unfeasible. Our calculations indicate that the three crossing points, respectively, between the A2Σ+ and a4Σ-, A2Σ+ and B2Σ-, and A2Σ+ and b4Π states of SH, all lie above the v' = 1 vibrational level of the A2Σ+ state, as a result of which the crossings involving electronic states of higher energy would not hinder its laser cooling. Based upon our study on various excited states, we have constructed a viable laser-cooling scheme for SH, utilizing three laser beams and leveraging the A2Σ+ → X2Π transition. This transition possesses a very large vibrational branching ratio R00 (0.9558), an abundant number of scattered photons (9.30 × 103), and a short radiative lifetime (787 ns). Our work underscores the important role of excited-state crossings in molecular laser cooling and demonstrates that SH emerges as a very good candidate for ultracold molecules.

Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof

Neural-network-supported basis optimizer for the configuration interaction problem in quantum many-body clusters: Feasibility study and numerical proof

Effective Hamiltonians from Spin-Adapted Configuration Interaction.

A generalized extraction procedure for magnetic interactions using effective Hamiltonians is presented that is applicable to systems with more than two sites featuring local spins Si ≥ 1. To this end, closed, nonrecursive expressions pertaining to chains of arbitrary equal spins are derived with the graphical method of angular momentum. The method is illustrated by extracting magnetic couplings from ab initio calculations on a [CaMn3(IV)O4] cubane. An extension to nonsequential coupling schemes proves conducive to expressing additional symmetries of certain spin Hamiltonians.

Full-Dimensional Neural Network Potential Energy Surface for the Photodissociation Dynamics of HNCS in the S1 band.

The full-dimensional potential energy surface (PES) for the photodissociation of HNCS in the S1(1A″) electronic state has been built up by the neural network method based on more than 48,000 ab initio points, which were calculated at the multireference configuration interaction level with Davidson correction using the augmented correlation consistent polarized valence triple-ζ basis set. It was found that two minima, namely, trans and cis isomers of HNCS, and seven stationary points exist on the S1 PES for the three dissociation pathways: HNCS(S1) → H + NCS/HNC + S(1D)/HN(1Δ) + CS(1Σ+). The dissociation energies of two lowest product channels H + NCS and HNC + S(1D) calculated on the PES are in good agreement with experimental results, validating the high accuracy of the PES. Furthermore, the quasi-classical trajectory calculations were carried out to investigate the photodissociation dynamics of HNCS(S1) at the total energy ranging from 5.0 to 6.0 eV based on the newly constructed S1 PES. It was found that two products H + NCS/HNC + S(1D) are dynamically comparable with the branching ratios of ∼1:1 at high energies, and the product HNC + S(1D) is favored at low energies, resulting from different topographies of the PES along the two dissociation pathways. Specifically, the translational energy distributions of the products H + NCS and HNC + S(1D) were found to be exceedingly different. The former behaves like a Gauss-type function with a broad width and a center of the peak at relatively high energy, while the latter is dominated by the low energies and decays heavily as the translational energy increases, shedding light on the photodissociation dynamics of HNCS in the S1 band.

An ab initio study of the rovibronic spectra of CH.

CH is one of the most spectroscopically studied diatomic molecules. The rovibronic spectra of the methylidyne radical (CH) in adiabatic and diabatic representations are obtained based on ab initio data, including 12 potential energy curves, 38 dipole moment curves, 79 spin-orbit coupling curves, and 18 electronic angular momentum coupling curves. We employed the internally contracted multireference configuration interaction method including the Davidson correction with the aug-cc-pV(5+d)Z basis set for the C atom and the aug-cc-pV5Z basis set for the H atom. The diabatic transformations are performed based on a property-based diabatisation method to remove the avoided crossings for the E 2Π-F 2Π and F 2Π-H 2Π pairs. The coupled nuclear motion Schrödinger equations are then solved using the Duo nuclear motion program to obtain the rovibronic spectra of CH for wavenumbers from 0 to 80 000 cm-1 at 5000 K. An overall prediction of the rovibronic spectra of CH is provided in this work. Our results could be beneficial for future calculations of rovibronic spectra of CH and contribute to improving astronomical, chemical, and physical models.

Structure of the Se4 Isomers─An Ab Initio Study.

This study investigates the equilibrium geometries of four different Se4 isomers using the coupled cluster single and double perturbative (CCSD(T)) method, extrapolating to the complete basis sets. The ground-state geometry of the Se4 isomer with the C2v structure (2.8715 Å, 2.1750 Å, and 88.4°) is found to be very close to other theoretical values (2.910 Å, 2.224 Å, and 90.0°) for the Se═Se and Se-Se bond lengths and valence angle. Additionally, the adiabatic electron affinity, vertical electron affinity, and vertical ionization energy are calculated. The multireference configuration interaction method was used to calculate transitions from the singlet ground state to some excited counterparts, including the vertical excitation energy, oscillator strength, and main electronic configuration. The predicted wavelengths of electronic transitions to 11Bu, 11Au with C2h symmetry, and 11B1 state with the C2V symmetry could match the experimental NIR absorption band at 710-850 nm. These transitions and electronic properties may provide insights into the role of selenium in astrophysical environments, where 74Se in the solar system has been confirmed to originate from the supernova explosion process. The theoretical results offer a deeper understanding of Se4 electronic and geometric structures while also providing crucial spectroscopic data that could aid in the identification of selenium-containing molecules in extraterrestrial environments.

Series expansion of a scalable Hermitian excitonic renormalization method.

Utilizing the sparsity of the electronic structure problem, fragmentation methods have been researched for decades with great success, pushing the limits of abinitio quantum chemistry ever further. Recently, this set of methods has been expanded to include a fundamentally different approach called excitonic renormalization, providing promising initial results. It builds a supersystem Hamiltonian in a second-quantized-like representation from transition-density tensors of isolated fragments, contracted with biorthogonalized molecular integrals. This makes the method fully modular in terms of the quantum chemical methods applied to each fragment and enables massive truncation of the state-space required. Proof-of-principle tests have previously shown that an excitonically renormalized Hamiltonian can efficiently scale to hundreds of fragments, but the ad hoc approach to building the Hamiltonian was not scalable to larger fragments. On the other hand, initial tests of the originally proposed modular Hamiltonian build, presented here, show the accuracy to be poor on account of its non-Hermitian character. In this study, we bridge the gap between these with an operator expansion that is shown to converge rapidly, tending toward a Hermitian Hamiltonian while retaining the modularity, yielding an accurate, scalable method. The accuracy is tested here for a beryllium dimer. At distances near equilibrium and longer, the zeroth-order method is comparable to coupled-cluster singles, doubles, and perturbative triples and the first-order method is comparable to full configuration interaction (FCI). The second-order method agrees with FCI for distances well up the inner repulsive wall of the potential. Deviations occurring at shorter bond distances are discussed along with approaches to scaling to larger fragments.

Double configuration interaction singles: Scalable and size-intensive approach for orbital relaxation in excited states and bond-dissociation

We present a novel theoretical scheme for orbital relaxation in configuration interaction singles (CIS) based on a perturbative treatment of its electronic Hessian, whose analytical derivation is also established in this work. The proposed method, which can be interpreted as a “CIS-then-CIS” scheme, variationally accounts for orbital relaxation in excited states, thus significantly reducing the overestimation of charge-transfer excitation energies commonly associated with standard CIS. In addition, by incorporating de-excitation effects from CIS, we demonstrate that our approach effectively describes single bond dissociation. Notably, all these improvements are achieved at a mean-field cost, with the pre-factor further reduced with the efficient algorithm introduced here, while preserving the size-intensive property of CIS.

ExoMol line lists – LXI. A trihybrid line list for rovibronic transitions of the hydroxyl radical (OH)

Abstract The hydroxyl radical (OH) is a species of high importance in exoplanetary studies, the interstellar medium, and in stellar spectra. Terrestrially it is a significant component of combustion chemistry, an oxidizer in the upper atmosphere, and a source of telluric bands. Internally contracted multi-reference configuration interaction potential energy curves (PECs), spin-orbit couplings, electronic angular momentum couplings, and (transition) dipole moments for eight electronic states of OH are computed and refined against empirical energy levels to produce an OH spectroscopic model. A line list consisting of rovibronic term values, allowed electronic dipole transitions, Einstein-A coefficients, and partition functions for varying temperature and a continuum absorption data set are then produced by variational solution of the coupled-channel Schrödinger equations using the nuclear motion code Duo. Marvel energy levels substitute equivalent levels in the OH line list, with estimated uncertainties in experimentally dark regions, following an established hybridization procedure. Predissociation lifetimes of the A 2Σ+ state are calculated using a stabilization method and convoluted with natural lifetimes to include predissociative effects. Continuum absorption cross sections for T ∈ [100, 200, ..., 8000] K and zero pressure are provided in the range of 0 → 80 000 cm−1 with a step size of 0.01 cm−1. Comparison with available literature cross sections exhibits strong agreement. The line list is suitable for high-resolution studies up to 8000 K. The OH MYTHOS dataset is available for download via www.exomol.com.

Role of the Radical Character in Singlet Fission: An Ab Initio and Quantum Chemical Topology Analysis.

The radical character of molecules exhibiting singlet fission is related to the energy level matching relationships that facilitate this process. Using a linear H4 model molecule, we employ quantum chemical topology descriptors based on full configuration interaction calculations to rationalize singlet fission. In this context, the influence of the closed-shell to diradical and diradical to tetraradical character on the singlet fission energy matching conditions is analyzed. We find that in the diradical limit the singlet fission efficiency can be manipulated considering the active molecule coupled to an excited diradical, while in the diradical to tetraradical limit, the efficiency is dependent only on the gap between the lowest-lying excited singlet and triplet state. Furthermore, our results reveal possible design strategies for molecules with radical character exhibiting efficient singlet fission.