An efficient internally contracted multiconfiguration–reference configuration interaction method

Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with a ground state that requires a multireference treatment. In this work, we introduce a novel equation-of-motion (EOM) extension of the internally contracted multireference unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows the transform-then-diagonalize approach, in analogy to its non-unitary counterpart [Datta and Nooijen, J. Chem. Phys. 137, 204107 (2012)]. By employing a projective approach to optimize the ground state, the method retains additive separability and proper scaling with system size. We show that excitation energies are size-intensive if the EOM operator satisfies the "killer" and the projective conditions. Furthermore, we propose to represent changes in the reference state upon electron excitation via projected many-body operators that span the active orbitals and show that the EOM equations formulated in this way are invariant with respect to active orbital rotations. We test the EOM-ic-MRUCC method truncated to single and double excitations by computing the potential energy curves for several excited states of a BeH2 model system, the HF molecule, and water undergoing symmetric dissociation. Across these systems, our method delivers accurate excitation energies and potential energy curves within 5 mEh (∼0.14 eV) from full configuration interaction. We find that truncating the Baker-Campbell-Hausdorff series to fourfold commutators contributes negligible errors (on the order of 10-5Eh or less), offering a practical route to highly accurate excited-state calculations with reduced computational overhead.

Theoretical study on the core-excited states of the allyl using multi-reference methods with core-valence separation (CVS) approximation

The multi-state n-electron valence second-order perturbation theory with core-valance separation (CVS) approximation (CVS-MS-NEVPT2) and static-dynamic-static multi-state multi-reference second-order perturbation theory with CVS (CVS-SDSPT2) were developed based on the internally contracted multi-reference configuration interaction method with single and double excitations with CVS (CVS-icMRCISD) [Song et al., J. Chem. Phys. 160, 094114 (2024)] due to their high similarity and inheritance in theoretical frameworks and computational implementation. Benchmark calculations demonstrate that these perturbation methods significantly improved computational efficiency while maintaining comparable accuracy to the CVS-icMRCISD method. Moreover, the core-excited states of the allyl system were used as a pilot application for three CVS-multi-reference methods. The CVS-icMRCISD method produced four excited states at 282.10, 285.11, 286.18, and 288.07 eV, accurately reproducing four distinctive peaks (A, B, C, and D) in the experimental x-ray absorption spectra (XAS). Theoretical excitation energies of two core-excited states of the allyl cation (282.64 and 286.88 eV) align with the peaks observed at 282.52 and 286.92 eV in the experimental XAS. However, vibrational analysis of the X-A transition suggests that the α band in the experimental XAS might arise from electronic-vibronic coupling between the antisymmetric stretching of C-H bonds in the -CTH2 group and the core-excited state, leaving the assignment of the α band ambiguous. Overall, the CVS-icMRCISD method achieved excellent agreement with experimental results, with an average deviation of 0.25 eV. While the errors of CVS-SDSPT2 and CVS-MS-NEVPT2 methods were slightly larger, both methods maintained acceptable accuracy, making them suitable for medium-sized molecules by significantly reducing computational costs.

Electronic quenching of N(2D) in collision with CO(1Σ+) via spin-forbidden transitions

In nitrogen-rich atmospheres under extreme conditions, the N2 molecule dissociates into atomic nitrogen in different electronic states. In particular, N(2D) is known to be reactive and to drive a complex chemistry in such regimes. If the atmosphere also contains carbon monoxide (such as Earth and Mars), several collisional processes with nitrogen-, carbon-, and oxygen-bearing species are relevant. Here, we employ a set of three accurate and global potential energy surfaces for the CNO system to study the N(2D) + CO → N(4S) + CO electronic quenching process, using the quasiclassical trajectories approach coupled with two different surface hopping schemes. Experimental measurements of the quenching rate coefficient are available only at room temperature, and our computational predictions show good agreement. We further provide the temperature dependence of the rate coefficients for the first time, extending to the hyperthermal regime. The effect of the initial rovibrational state of CO on the reactivity, as well as the distribution of energy in the products, is also unveiled.

Semiclassical Approach to Computing Vibrationally Resolved Ionization Cross Sections for Molecular Nitrogen

A semiclassical model based on the Gryzinski theory is used to compute vibrationally resolved electron-impact ionization cross sections for molecular nitrogen. This model extends the approach used by Wünderlich for molecular hydrogen and its isotopomeres. The multireference configuration interaction (MRCI) method in Molpro is used with complete active space self-consistent field reference wave functions to compute potential energy curves (PECs) and electronic wave functions for several states of interest. Nuclear wave functions and vibrational energy levels are computed from the MRCI PECs using the Fourier grid Hamiltonian method. The target orbital electron kinetic energies, Franck-Condon factors, and transition energies are parameters for the semiclassical model and are calculated directly from the computed electronic and nuclear wave functions and vibrational energy levels. The target electron kinetic energies are computed as the expectation value of the one-electron kinetic energy operator for the product of the appropriate nuclear vibrational wave function and the MRCI natural orbital for a particular state-to-state ionization process. From the fully vibrationally resolved ionization cross sections, lumped and total cross sections are calculated by summing the partial cross sections over the closure relationship of the Franck-Condon theory.

P[triple bond, length as m-dash]B and As[triple bond, length as m-dash]B triple bonds in the linear PB2O- and AsB2O- species

Due to its electron deficiency, boron triple bonds are relatively scarce. We use high-resolution photoelectron imaging to investigate the structures and bonding of the EB2O- (E = P, As) type of clusters, which are found to have [E[triple bond, length as m-dash]B-B[triple bond, length as m-dash]O]- closed-shell linear structures with E[triple bond, length as m-dash]B triple bonds. The B atoms in the linear EB2O- species undergo sp hybridization, while the E atoms also undergo sp hybridization to form a σ bond with the sp orbital of B along with two π bonds formed by the p x and p y orbitals. The high-resolution photoelectron imaging data reveal detachment transitions from the EB2O- (1Σ+) anions to the EB2O (2Π) neutrals. The electron affinities of PB2O and AsB2O are measured to be 3.592(1) eV and 3.432(1) eV, respectively; the vibrational frequencies for the E-B, B-B, and B-O stretching modes are measured for both species. The spin-orbit splitting of the 2Π state to 2Π3/2 and 2Π1/2 is measured to be 153 cm-1 and 758 cm-1 for PB2O and AsB2O, respectively.

Conical Intersections Studied by the Configuration-Interaction-Corrected Tamm-Dancoff Method

Conical intersections directly mediate the internal energy conversion in photoinduced processes in a wide range of chemical and biological systems. Because of the Brillouin theorem, many conventional electronic structure methods, including configuration interaction with single excitations from a Hartree-Fock reference and time-dependent density functional theory in either the linear response approximation (TDDFT) or Tamm-Dancoff approximation (DFT-TDA), have the wrong dimensionality for conical intersections between the ground state (S0) and the first excited state (S1) of the same multiplicity. This leads to unphysical state crossings. Here, we implement and assess the configuration-interaction-corrected Tamm-Dancoff approximation (CIC-TDA) that restores the correct dimensionality of conical intersections by including the coupling between the reference state and the intersecting excited state. We apply the CIC-TDA method to the S1/S0 conical intersections in ammonia (NH3), ethylene (C2H4), bithiophene (C8H6S2), azobenzene (C12H10N2), and 11-cis retinal protonated Schiff base (PSB11) in vacuo. We show that this black-box approach can produce potential energy surfaces (PESs) of comparable accuracy to multireference wave function methods. The method validated here can allow cost-efficient explorations of photoinduced electronically nonadiabatic dynamics, especially for large molecules and complex systems.

Efficient Implementation of Approximate Fourth Order N-Electron Valence State Perturbation Theory

In this work, the implementation of a partial fourth order N-electron-valence perturbation theory (NEVPT) is reported and numerically evaluated. The method, termed NEVPT4(SD), includes the internally contracted functions that span the first-order-interacting space (FOIS) and evaluates their contribution to second-order in the wave function and fourth order in the energy. The triple- and quadruple excitations that would additionally enter the second-order-interacting space (SOIS) are not included. As discussed by Grimme [Chem. Phys. Lett. 2001, 334, 99-106] in order to obtain a size-consistent method, it is necessary to also drop the fourth-order renormalization term if the quadruple excitations are dropped. The NEVPT4(SD) method is demonstrated to be perfectly size consistent. Computationally, the method is still fairly affordable and requires about the same time as a single iteration of the fully internally contracted (FIC) MRCI or MRCEPA(0) and significantly cheaper than the FIC MRCC that serves as the reference for our calculations. The accuracy tests show that NEVPT4(SD) offers significant accuracy improvements over NEVPT2 for transition metal atom/ion multiplets as well as diatomic bond breaking potential energy surfaces. We find that going to fourth order in perturbation theory essentially eliminates the need for a second d-shell, thus showing that the latter primarily serves to capture higher-order dynamic correlation effects that are not present in a second-order treatment. Although it captures fourth-order correlation effects, NEVPT4(SD) is numerically not a large improvement over NEVPT2 for the calculation of Heisenberg exchange couplings as illustrated by test calculations on Cu(II) dimers.

Modeling the time-resolved Coulomb explosion imaging of halomethane photodissociation with ab initio potential energy curves

We present an effective theoretical model to simulate observables in time-resolved two-fragment Coulomb explosion experiments. The model employs the potential energy curves of the neutral molecule and the doubly charged cation along a predefined reaction coordinate to simulate the photodissociation process followed by Coulomb explosion. We compare our theoretical predictions with pump-probe experiments on iodomethane and bromoiodomethane. Our theory successfully predicts the two reaction channels in iodomethane photodissociation that lead to I(P3/22) and I*(P1/22) products, showing excellent agreement with experimental delay-dependent kinetic energy release signals at large pump-probe delays. The theoretical kinetic energy release at small delays depends significantly on the choice of ionic states. By accounting for internal rotation, the kinetic energies of individual fragments in bromoiodomethane align well with experimental results. Furthermore, our theory confirms that two-fragment Coulomb explosion imaging cannot resolve different spin channels in bromoiodomethane photodissociation.

Universal Framework for Multiconfigurational DFT

Strong correlation remains a significant challenge for DFT with no satisfying solutions found yet within the standard Kohn-Sham framework. Instead, for decades, a number of different approaches have been suggested to combine the accuracy of multiconfigurational methods with the efficiency of DFT. In this article, we demonstrate that many of these methods are or would be significantly improved by being reformulated as variants of multiconfigurational pair-density functional theory (MC-PDFT). This work presents the first implementation of these methods within the recently proposed variational formulation of MC-PDFT. It also provides for the first time a systematic comparison of their accuracy across representative examples of strongly correlated systems. By analyzing their accuracy and formal properties, we provide design guidelines to inform the development of future functionals.

Prediction of 57Fe Mössbauer Nuclear Quadrupole Splittings with Hybrid and Double-Hybrid Density Functionals

As a crucial parameter in Mössbauer spectroscopy, nuclear quadrupole splitting (NQS) exhibits a strong dependence on quantum chemistry methods, which makes accurate theoretical predictions challenging. Meanwhile, the continuous emergence of new density functionals presents opportunities to advance current NQS research. In this study, we evaluate the performance of eleven hybrid density functionals and twelve double-hybrid density functionals, selected from widely used functionals and newly developed functionals, in predicting the NQS values of the 57Fe nuclide for 32 iron-containing molecules within about 70 atoms. The calculations have incorporated scalar relativistic effects using the exact two-component (X2C) Hamiltonian. In general, the double-hybrid functional PBE-0DH demonstrates superior performance compared to the experimental values, achieving a mean absolute error (MAE) of 0.20 mm/s. Meanwhile, rSCAN38 is the best hybrid functional for our database with an MAE = 0.25 mm/s, and it offers a significant advantage in computational efficiency over PBE-0DH. The +/- sign of NQS has also been considered in our error statistics when it has a clear physical meaning; if neglected, the errors of many functionals decrease, but PBE-0DH and rSCAN38 remain unaffected. Notably, when calculating ferrocene [Fe(C5H5)2], which involves strong static correlations, all hybrid functionals that incorporate more than 10% exact exchange fail, while several double-hybrid functionals continue to deliver reliable results. In addition, we encountered two particularly challenging species characterized by strong static correlations: [Fe(H2O)5NO]2+ and FeO2--porphyrin. Unfortunately, none of the density functionals tested in our study yielded satisfactory results for the two cases since the density functional theory (DFT) is a single-determinant approach, and it is imperative to explore large-scale multi-configurational methods for these species. This research offers valuable guidance for selecting density functionals in Mössbauer NQS calculations and serves as a reference point for the future development of new density functionals.

Insights into facile methane activation by a spin forbidden reaction with Ta+ ions in the gas phase

The activation of methane (CH4) by transition-metal cations in the gas phase provides a model for understanding the impact of electronic spin on reactivity, with implications in single atom catalysis. In this work, we present a mixed quantum-classical trajectory surface hopping study on the nominally spin-forbidden reaction Ta+ + CH4 → TaCH2 + + H2. To facilitate the dynamics calculations, full twelve-dimensional PESs for three low-lying spin (quintet, triplet, and singlet) states are constructed using a machine learning method from density functional theory data. Furthermore, we report the temperature dependence of the rate coefficients for the Ta+ + CH4 → TaCH2 + + H2 reaction measured using the selected ion flow tube (SIFT) technique. The measured rate coefficient has a near zero temperature dependence and is approximately 50% of the capture limit at room temperature. Our theoretical results with a Gaussian-binning treatment of the product zero-point energy reproduced the experimental rate coefficient and the temperature dependence. Satisfactory agreement is also obtained between theory and differential cross sections measured recently using molecular beams combined with velocity map imaging. Specifically, our multi-state calculations confirm the indirect mechanism of this reaction with long-lived reaction intermediate after passing through the initial barrier and reveal that the kinetic bottleneck in this reaction is intersystem crossing between the quintet and triplet states. Furthermore, the energy disposal in the TaCH2 + (both singlet and triplet) and H2 products is found to be largely statistical due to the long lifetime of the exit-channel complex.

Effective Electron-Vibration Coupling by Ab Initio Methods

The description of electron-phonon coupling in materials is complex, with varying definitions of coupling constants in the literature and different theoretical approaches available. This article analyzes different levels of theory to introduce and compute these coupling constants. Within the quasi-particle picture, we derive an effective linear-coupling Hamiltonian, describing the interaction of electronic quasi-particles with vibrations. This description allows a comparison between coupling constants computed using density functional theory and higher-level quasi-particle approaches by identifying the Kohn-Sham potential as an approximation to the frequency-independent part of the self-energy. We also investigate their dependence on the exchange-correlation (XC) functional. Despite significant deviations of the Kohn-Sham eigenvalues, which arise from different XC functionals, the resulting coupling constants are remarkably similar. A comparison to quasi-particle methods, such as the well-established G0W0 approach, reveals significant quasi-particle weight renormalization. Surprisingly, however, in nearly all the considered cases, the coupling constants computed in the DFT framework are excellent approximates of the ones in the quasi-particle framework, which is traced back to a significant cancellation of competing terms. Other quasi-particle methods, such as the Outer Valence Green's Function approach and the ΔSCF method, are also included in the comparison. Moreover, we investigate the coupling of vibrations to excitonic excitations and find, by comparison to time-dependent density functional theory and extended multiconfiguration quasi-degenerate second-order perturbation theory, that knowing the underlying electron- and hole-vibration couplings is sufficient to accurately determine the exciton-vibration coupling constants in the studied cases.

The Electronic Structure and Bonding in Some Small Molecules

The electronic structures of the first- and second-row homonuclear diatomics, XeF2, and the weakly bound dimers of nitric oxide and nitrogen dioxide molecules in their ground states are discussed in terms of molecular orbital (MO) theory and, where possible, valence bond theories. The current work is extended and supported by restricted and unrestricted Hartree-Fock (RHF and UHF) self-consistent field (SCF), complete active space SCF (CASSCF), multi-reference configuration interaction (MRCI), coupled cluster CCSD(T), and unrestricted Kohn-Sham (UKS) density functional calculations using a polarized triple-zeta basis. The dicarbon (C2) molecule is especially poorly described by RHF theory, and it is argued that the current MO theories taught in most undergraduate courses should be extended in recognition of the fact that the molecule requires at least a two-configuration treatment.

Dynamics Study of the CaC (X3∑-) + C(3Pg) → Ca+C2 (∑v) Reaction: Based on a Full-Dimensional Neural Network Potential Energy Surface of CaC2

The CaC2 molecule, as an interstellar species that has already been detected, has attracted significant attention. To date, studies on the potential energy surface (PES) and the reaction dynamics of CaC2 are largely lacking. In this work, ab initio energy values were obtained for 3877 configurations using the icMRCI+Q method, and these energies were subsequently fitted using a neural network approach. During parameter optimization, the trust region framework (TRF) method, which has superior performance compared to the previously used Levenberg-Marquardt (LM) method, was used. The root-mean-squared error (RMSE) for both the training and testing sets meets the requirement for chemical accuracy (error less than 1 kcal/mol). Using the neural network PES, we identified one stable structure and two metastable structures for the ground state (X̃1A') of CaC2. The stable structure is T-shaped, while the two metastable structures are linear. The potential well depths of the stable structure and the two metastable structures are -10.98, -9.75, and -4.70 eV, respectively. Based on the obtained full-dimensional neural network PES, we investigated the CaC(X3Σ-) + C(3Pg) → Ca + C2 (Σv) reaction dynamics under different initial conditions. Under the condition that all other parameters remain unchanged, the reaction cross section and rate constant were found to be largest when the initial condition was v = 0 and j = 0. These findings indicate that the reaction rate is fastest when the CaC molecule is in its ground state.

Characterization of the electronic structure and fate of doubly ionized carbon diselenide

Single photon double ionization of carbon diselenide ([Formula: see text]) has been investigated by means of multi-particle coincidence techniques. The interpretation of the experimental spectra is helped by post-Hartree-Fock computations at the Coupled Clusters and Multi-Reference Configuration-Interaction levels to determine the energetics and electronic state potentials of [Formula: see text] and its fragments. The lowest experimental double ionization energy of [Formula: see text] has been found to be 24.68 ± 0.20 eV, reflecting the [Formula: see text] ground state, and is in agreement with the theoretical vertical double ionization energy of 24.41 eV. Several fragmentation channels are reported including experimental appearance energies and kinetic energy releases in comparison to theoretical results on their characteristics. In particular, we identify several purely repulsive, Coulomb explosion fragmentation channels.

Characterizing the photodissociation dynamics of HPCO in the S1 band

A full-dimensional potential energy surface (PES) represented by the neural network method for the first excited state S1(1A″) of HPCO is reported for the first time. The PES was constructed based on more than 51 000 ab initio points, which were calculated at the multi-reference configuration interaction level with Davidson correction using the augmented correlation consistent polarized valence triple zeta basis set. Based on the newly constructed PES, quasi-classical trajectory calculations were carried out to study the photodissociation dynamics of HPCO at the total energy ranging from 4.0 to 5.6 eV. At low total energies, the HP + CO product is dominant, while the product H + PCO becomes increasingly favored at higher energies. Furthermore, the translational energy distributions of two products are found to be energy-dependent. Owing to the strongly repulsive PES along the HP + CO dissociation pathway, the translational energy distributions of HP + CO are dominated by relatively higher energies in contrast to H + PCO. The diatomic products HP and CO are found to possess the vibrational distributions decaying monotonically with the vibrational quantum number and relatively cold rotational state distributions, consistent with the strongly repulsive potentials toward the HP + CO channel. In addition, the vibrational distributions of HP and CO are found to be quite similar due to their close frequencies, while the rotational distributions of CO have a much more highly excited rotational degree of freedom owing to its rotational constant approximately four times smaller than that of HP.

Ab Initio Valence Bond Molecular Dynamics: A Study of SN2 Reaction Mechanisms

In this paper, a molecular dynamics (MD) approach based on ab initio classical valence bond (VB) theory, referred to as AIVBMD, is presented. To validate AIVBMD, a novel algorithm that enables efficient computation of energy gradients based on nonorthogonal orbitals is introduced. Taking the gas-phase SN2 reaction as an example, a compact VB wave function gives reasonable accuracy with only 27 VB structures, compared to the full active space of 5292 VB structures. Furthermore, AIVBMD provides intuitive chemical insights into the reaction process, detailing the breaking and formation of chemical bonds, thereby elucidating the reaction mechanism. In summary, as the first attempt at the ab initio classical VB method-based MD approach, this paper demonstrates that VB theory offers a novel perspective and significant potential for investigating chemical reaction dynamics and mechanisms.

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.

Minimum Energy Conical Intersection Optimization Using DFT/MRCI(2)

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method is a semiempirical electronic structure approach that is both computationally efficient and has predictive accuracy for the calculation of electronic excited states and for the simulation of electronic spectroscopies. However, given that the reference space is generated via a selected-CI procedure, a challenge arises in the construction of smooth potential energy surfaces. To address this issue, we treat the local discontinuities that arise as noise within the Gaussian progress regression framework and learn the surfaces by explicitly incorporating and optimizing a white-noise kernel. The characteristic polynomial coefficient surfaces of the potential matrix, which are smooth functions of nuclear coordinates even at conical intersections, are learned in place of the adiabatic energies and are used to optimize the DFT/MRCI(2) minimum energy conical intersection geometries for representative intersection motifs in the molecules ethylene, butadiene, and fulvene. One consequence of explicitly treating the noise in the surfaces is that the energy difference cannot be made arbitrarily small at points of nominal intersection. Despite the limitations, however, we find the structures as well as the branching spaces to compare well with ab initio MRCI and conclude that this approach is a viable method to learn a smooth representation of DFT/MRCI(2) surfaces.

Quantum control of ion-atom collisions beyond the ultracold regime

Tunable scattering resonances are crucial for controlling atomic and molecular systems. However, their use has so far been limited to ultracold temperatures. These conditions remain hard to achieve for most hybrid trapped ion-atom systems-a prospective platform for quantum technologies and fundamental research. Here, we measure inelastic collision probabilities for Sr+ + Rb and use them to calibrate a comprehensive theoretical model of ion-atom collisions. Our theoretical results, compared with experimental observations, confirm that quantum interference effects persist to the multiple-partial-wave regime, leading to the pronounced state and mass dependence of the collision rates. Using our model, we go beyond interference and identify a rich spectrum of Feshbach resonances at moderate magnetic fields with the Rb atom in its lower (f = 1) hyperfine state, which persist at temperatures as high as 1 millikelvin. Future observation of these predicted resonances should allow precise control of the short-range dynamics in Sr+ + Rb collisions under unprecedentedly warm conditions.

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.

Excited electronic states of Na2 and K2: The potential for long-lived "reservoir" states leading to collision induced population inversions

Potential energy curves (PECs) for the spin-free (ΛS) and spin-orbit (Ω) states associated with the four lowest-lying dissociation channels of Na2 and K2 were calculated at the SA-CASSCF/SO-CASPT2/aug-cc-pwCVQZ-DK level. The PECs of Na2 were consistent with the experimental data and with the FS-CCSD (2,0) calculations, reproducing the double-well and the "shelf" character for some of the potentials of the excited states. For K2, the PECs behaved in a similar way and the spectroscopic parameters for the ground and the excited states are in good agreement with the available experimental values. The dissociation energy of K2 was predicted to be De = 4454 cm-1, within an agreement of 5 cm-1 with the experiments. For Na2, De = 5789 cm-1 compared to the experimental value of 6022 cm-1. The inclusion of spin-orbit coupling effects resulted in avoided crossings, which affect the PECs. Spin-orbit changes the predicted curves for some excited Ω states arising from ΛS states that overlap each other, affecting their associated vibrational frequencies and bond distances. The current studies of the low-lying states in K2 reveal a similar structure to those of Na2, which suggests the accessibility of long-lived energy storing reservoir states and possible population inversions in K2 following prior experimental work on the reaction of halogen atoms with Na3 to produce excited states of Na2.

Association Kinetics for Perfluorinated n-Alkyl Radicals

Radical-radical reaction channels are important in the pyrolysis and oxidation chemistry of perfluoroalkyl substances (PFAS). In particular, unimolecular dissociation reactions within unbranched n-perfluoroalkyl chains, and their corresponding reverse barrierless association reactions, are expected to be significant contributors to the gas-phase thermal decomposition of families of species such as perfluorinated carboxylic acids and perfluorinated sulfonic acids. Unfortunately, experimental data for these reactions are scarce and uncertain. Furthermore, obtaining reliable theoretical predictions for such reactions is a laborious and computationally intensive task. In this work, the chemical kinetics of the various association/decomposition reactions producing/decomposing the C2-C4 series of unbranched n-perfluoroalkanes (C2F6, C3F8, and C4F10) are examined using state-of-the-art ab initio transition-state-theory-based master-equation calculations. The variable-reaction-coordinate transition-state theory (VRC-TST) formalism is employed in computing the microcanonical and canonical rates for the association reactions. Reaction thermochemistry is obtained via composite quantum chemistry calculations and the laddering of error-canceling reaction schemes via a connectivity-based hierarchy approach employing ANL1/ANL0-style reference energies. Lennard-Jones collision model parameters for the considered systems were estimated by a direct dynamics approach, and collisional energy transfer parameters were obtained from analogies to systems of similar size and heavy-atom connectivity. A one-dimensional master equation approach was used to convert the microcanonical rate coefficients from the VRC-TST analysis into temperature- and pressure-dependent rate constants for the association reactions and the reverse dissociation reactions. The data are reported in standardized formats for usage in comprehensive chemical kinetic models for PFAS thermal destruction.

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.

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 [Formula: see text] and [Formula: see text] transitions are both calculated. The results indicated that the radiative lifetimes of the [Formula: see text] and [Formula: see text] 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.

Ab initio electronic structures and total internal partition sums of FeH+/2

In the present work, we studied 27 FeH+ and 6 FeH2+ electronic states using multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), and coupled cluster singles doubles and perturbative triples [CCSD(T)] wavefunction theory (WFT) calculations conjoined with large quadruple-ζ and quintuple-ζ quality correlation consistent basis sets. We report their potential energy curves (PEC), energy related properties, spectroscopic parameters, and spin-orbit couplings. Dipole moment curves (DMC) and transition dipole moment curves (TDMC) of several low-lying electronic states of FeH+ and FeH2+ are also introduced. The ground state of FeH+ is a single-reference X5Δ (6σ27σ13π21δ3) with an adiabatic D0 of ∼52 kcal mol-1, which is in agreement with the experimental value. The states with the largest adiabatic binding energies of FeH2+ (4Π and 4Δ) are multireference in nature with an approximate D0 of 22 kcal mol-1. We used CCSD(T) μ of the FeH+(X5Δ) to assess the density functional theory (DFT) errors associated with a series of functionals that span multiple rungs of Jacob's ladder of density functional approximation (DFA) and observed a general trend of improving μ when moving to more expensive functionals at the higher rungs. We expect weak spectral bands to be produced from the low-lying electronic states of FeH2+ and FeH+ due to their lower transition μ values. Lastly, we present results for the total internal partition function sums (TIPS) of FeH+ and FeH2+, which have not been presented in the literature before.

Thermodynamic Stability in Transition Metal-Hydrogen Dications: Potential Energy Curves, Spectroscopic Parameters, and Bonding for VH2. J Comput Chem 2025;46:e27530. [PMID: 39754406 DOI: 10.1002/jcc.27530] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Seventeen electronic states of the dication VH2+ were characterized by the SA-CASSCF/icMRCI methodology using very extended basis sets; 11 were described for the first time. Potential energy curves were constructed and the associated spectroscopic parameters evaluated. Triplet and quintet states correlating with the V2+ + H channel are thermodynamic stable. For states dissociating into the channel V+ + H+, avoided crossings at large distances give rise to thermodynamic metastability but do not affect the characterization of the bound region. Configuration state functions with the 3σ orbital /doubly occupied give rise to covalent contributions to the bonding; the major contribution, however, comes from the electrostatic charge-induced dipole interaction. This explains the shape and proximity of the potential energy curves beyond their equilibrium distances. Dipole moment functions and vibrationally averaged dipole moments quantify the polarity of the molecule. Spin-orbit couplings give rise to complex and dense regions of very close-lying Ω states.

Best-of-both-worlds computational approaches to difficult-to-model dissociation reactions on metal surfaces

The accurate modeling of dissociative chemisorption of molecules on metal surfaces presents an exciting scientific challenge to theorists, and is practically relevant to modeling heterogeneously catalyzed reactive processes in computational catalysis. The first important scientific challenge in the field is that accurate barriers for dissociative chemisorption are not yet available from first principles methods. For systems that are not prone to charge transfer (for which the difference between the work function of the surface and the electron affinity of the molecule is larger than 7 eV) this problem can be circumvented: chemically accurate barrier heights can be extracted with a semi-empirical version of density functional theory (DFT). However, a second important challenge is posed by systems that are prone to (full or partial) electron transfer from the surface to the molecule. For these systems the Born-Oppenheimer approximation breaks down, and currently no method of established accuracy exists for modeling the resulting effect of non-adiabatic energy dissipation on the dissociative chemisorption reaction. Because two problems exist for this class of reactions, a semi-empirical approach to computing barrier heights, which would demand that computed and experimental dissociative chemisorption probabilities match, is unlikely to work. This Perspective presents a vision on how these two problems may be solved. We suggest an approach in which parameterized density functionals are used as in the previous semi-empirical approach to DFT, but in which the parameters are based on calculations with first principles electronic structure methods. We also suggest that the diffusion Monte-Carlo (DMC) and the random phase approximation (RPA) probably are the best two first principles electronic structure methods to pursue in the framework of the approach that we call first-principles based DFT (FPB-DFT) - providing DMC and the RPA with a steppingstone towards benchmarking and future applications in computational catalysis. Probably the FPB density functional is best based on screened hybrid exchange in combination with non-local van der Waals correlation. We also propose a new electronic friction method called scattering potential friction (SPF) that could combine the advantages and avoid the disadvantages of the two main existing electronic friction approaches for describing non-adiabatic effects: by extracting an electronic scattering potential from a DFT calculation for the full molecule-metal surface system, it might be possible to compute friction coefficients from scattering phase shifts in a computationally convenient and robust fashion. Combining the FPB-DFT and SPF methods may eventually result in barrier heights of chemical accuracy for the difficult-to-model class of systems that are prone to charge transfer. This should also enable the construction of a representative database of barrier heights for dissociative chemisorption on metal surfaces. Such a database would allow testing new density functionals, or, more generally, new electronic structure approaches on a class of reactions that is of huge importance to the chemical industry. Additionally, the difficult-to-model sub-class of systems we focus on is essential to sustainable chemistry and important for a sustainable future. Adding the database envisaged to large databases already existing but mostly addressing gas phase chemistry will enable testing density functionals that have a claim to universality, i.e., to be good for all chemical systems of importance. We also make a suggestion for how to develop such a generally applicable functional, which should have the correct asymptotic dependence of the exchange contribution to the energy in both the gas phase and the metal. Finally we suggest some improvements in the representation of potential energy surfaces and in dynamics methods that would help with the validation of the proposed methods.

Theoretical Study on the Spectroscopic Properties and Line Intensities of the O2+ Cation

O2+ cation, as one of the major gas components in the near space environment, has attracted significant attention due to its spectroscopic properties. In this study, we systematically investigate the spectroscopic properties of the O2+ cation using ab initio methods. The potential energy curves and transition dipole moments of O2+ were obtained using the icMRCI + Q method combined with the ACV5Z-DK basis set. Subsequently, the vibrational and rotational energy levels, as well as the corresponding spectroscopic constants for both ground and excited states, were determined by solving the one-dimensional radial Schrödinger equation. Based on the vibrational and rotational energy levels of bound electronic states, the internal partition function of O2+ was computed over the temperature range of 100-10,000 K. Utilizing the precise potential energy functions, transition dipole moment functions, and internal partition functions, the line intensities for the First Negative Band System (a4Πu-b4Σg-) and the Second Negative Band System (X2Πg-A2Πu) were calculated. For the first negative band system, the spectral line intensity of Δν = 1 is maximized at temperatures ranging from 100 to 7000 K. In the case of the second negative band system, the strongest vibrational band shifts with increasing temperature. We also discuss the impact of temperature on spectral lines; at higher temperatures, a greater number of energy levels are populated, allowing for the observation of more spectral lines. These findings are significant for understanding the spectral behavior of high-temperature nonequilibrium plasmas and their role during spacecraft reentry, providing a theoretical basis for experimental research.

Photodissociation of the CH2Cl radical: A high-level ab initio study

Photodissociation of the CH2Cl radical is investigated by using high-level multireference configuration interaction ab initio methods, including the spin-orbit coupling. All possible fragmentation pathways, namely, CH2Cl + hν → CH2 + Cl, HCCl + H, and CCl + H2, have been analyzed. The potential-energy curves of the ground and several excited electronic states along the corresponding dissociating bond distance of each pathway have been calculated. Inclusion of the spin-orbit couplings is found to be crucial because it strongly determines the shape of the curves of the different excited states and, therefore, their photodissociation dynamics behavior. Analysis of the potential curves indicates that the pathways producing CH2 + Cl and HCCl + H can occur through a fast direct dissociation mechanism, while the pathway leading to CCl + H2 involves much slower dissociation mechanisms such as internal conversion between electronic states, predissociation, or tunneling through exit barriers. The main implications are that the two faster channels are predicted to be dominant, while the slower pathway is expected to be very unlikely and rather irrelevant. Appreciable actinic fluxes of solar irradiation are available at stratospheric altitudes where ozone is abundant, in the wavelength range where absorption of the first low-lying excited states of CH2Cl has been observed experimentally. Our results show that in this excitation energy range, the above-mentioned two dominant dissociation pathways are open and then could contribute to stratospheric ozone depletion.

State-to-State Time-Dependent Quantum Dynamics Studies of the Si(3P) + OH(X 2Π) → OSi(X 1Σg+) + H(2S) Reaction Based on a New HOSi(X2A') Potential Energy Surface

Quantum and quasi-classical dynamics calculations were conducted for the reaction of Si with OH on the latest potential energy surface (PES), which is obtained by fitting tens of thousands of ab initio energy points by using the many-body expansion formula. To obtain an accurate PES, all energy points calculated with aug-cc-pVQZ and aug-cc-pV5Z basis sets were extrapolated to the complete basis set limit. The accuracy of our new PES was verified by comparing the topographic characteristics and contour maps of potential energy with other works. In addition, the anharmonic vibrational frequencies of HOSi and HSiO based on the present ab initio and PES by means of quantum dynamics methods were calculated. Dynamics information such as reaction probability, integral cross sections (ICS), product distribution, and rate constants was obtained on the new HOSi(X2A') PES. The dynamic information calculated using the quasi-classical trajectory method and time-dependent wave packet method is generally in good agreement, except for the vibrational state-resolved ICSs of product. The calculated differential cross section and capture time reveal that the reaction is primarily governed by the complex formation mechanism.

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.

Nature of the Nickel-Halogen Bond in NiX+ Compounds (X = F, Cl, Br, I): A Multireference Configuration Interaction and Ab Initio Valence Bond Study

In a recent study (Inorg. Chem. 2024, 63, 11812-11820), gas-phase cationic NiX+ compounds (X = F, Cl, Br, and I) were probed by nickel L-edge XAS, from which it was concluded that NiF+ was best described as an ionic [Ni2+F-]+ complex while the remaining three compounds were described as covalent Ni(3d9)L species (L depicts a ligand-based hole). An abrupt transition from a classical to an inverted ligand field was suggested as responsible for the change in ground-state electronic structures. Herein, the NiX+ series is investigated by using MRCI and ab initio VB calculations. Nickel L-edge X-ray absorption spectra were also modeled within a ROCIS formalism. It was found that all four compounds possess normal ligand fields and nominal Ni(3d9) electron counts. Furthermore, it was found that the dominant bonding interactions in NiF+ and NiCl+ are two 2-center/3-electron (2c/3e) bonds, while in NiBr+ and NiI+ the dominant bonding interactions are one Ni-X covalent bond and one 2c/3e bond. The change in bonding interactions between NiF+/NiCl+ vs NiBr+/NiI+ was rationalized by considering the marked decrease in resonance energy that stabilizes the 2c/3e bond for the heavier halide congeners, which results from the disparity in electronegativities between the nickel-center and the heavier halides.

Equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting approximation: An efficient implementation

Orbital-optimized coupled-cluster methods are very helpful for theoretical predictions of the molecular properties of challenging chemical systems, such as excited states. In this research, an efficient implementation of the equation-of-motion orbital-optimized coupled-cluster doubles method with the density-fitting (DF) approach, denoted by DF-EOM-OCCD, is presented. The computational cost of the DF-EOM-OCCD method for excitation energies is compared with that of the conventional EOM-OCCD method. Our results demonstrate that DF-EOM-OCCD excitation energies are dramatically accelerated compared to EOM-OCCD. There are almost 17-fold reductions for theC 5 H 12 molecule in an aug-cc-pVTZ basis set with the RHF reference. This dramatic performance improvement comes from the reduced cost of integral transformation with the DF approach and the efficient evaluation of the particle-particle ladder (PPL) term, which is the most expensive term to evaluate. Further, our results show that the DF-EOM-OCCD approach is very helpful for the computation of excitation energies in open-shell molecular systems. Overall, we conclude that our new DF-EOM-OCCD implementation is very promising for the study of excited states in large-sized challenging chemical systems.

Importance of Electron Correlation on the Geometry and Electronic Structure of [2Fe-2S] Systems: A Benchmark Study of the [Fe2S2(SCH3)4]2-,3-,4-, [Fe2S2(SCys)4]2-, [Fe2S2(S-p-tol)4]2-, and [Fe2S2(S-o-xyl)4]2- Complexes

Iron-sulfur clusters are crucial for biological electron transport and catalysis. Obtaining accurate geometries, energetics, manifolds of their excited electronic states, and reduction energies is important to understand their role in these processes. Using a [2Fe-2S] model complex with FeII and FeIII oxidation states, which leads to different charges, i.e., [Fe2S2(SMe)4]2-,3-,4-, we benchmarked a variety of computational methodologies ranging from density functional theory (DFT) to post-Hartree-Fock methods, including complete active space self-consistent field (CASSCF), multireference configuration interaction, the second-order N-electron valence state perturbation theory (NEVPT2), and the linearized integrand approximation of adiabatic connection (AC0) approaches. Additionally, we studied three experimentally well-characterized complexes, [Fe2S2(SCys)4]2-, [Fe2S2(S-o-tol)4]2-, and [Fe2S2(S-o-xyl)4]2-, via DFT methods. We conclude that the dynamic electron correlation is important for accurately predicting the geometry of these complexes. Broken symmetry (BS) DFT correctly predicts experimental geometries of low-spin multiplicity, while CASSCF does not. However, BS-DFT significantly overestimates the difference between the low- and high-spin electronic states for a given oxidation state. At the same time, CASSCF underestimates it but provides relative energies closer to the reference NEVPT2 results. Finally, AC0 provides energetics of NEVPT2 quality with the additional advantage of being able to use large CASSCF sizes. NEVPT2 gives the best estimates of the FeIII/FeIII → FeII/FeIII (4.27 eV) and FeII/FIII → FeII/FII (7.72 eV) reduction energies. The results provide insight into the electronic structure of these complexes and assist in the understanding of their physical properties.

Spectroscopic signatures and origin of hidden order in Ba2MgReO6

Clarifying the underlying mechanisms that govern ordering transitions in condensed matter systems is crucial for comprehending emergent properties and phenomena. While transitions are often classified as electronically driven or lattice-driven, we present a departure from this conventional picture in the case of the double perovskite Ba2MgReO6. Leveraging resonant and non-resonant elastic x-ray scattering techniques, we unveil the simultaneous ordering of structural distortions and charge quadrupoles at a critical temperature of Tq ~ 33 K. Using a variety of complementary first-principles-based computational techniques, we demonstrate that, while electronic interactions drive the ordering at Tq, it is ultimately the lattice distortions that dictate the specific ground state that emerges. Our findings highlight the crucial interplay between electronic and lattice degrees of freedom, providing a unified framework to understand and predict unconventional emergent phenomena in quantum materials.

Force-Assisted Orbital Crossing in Mechanochemical Oxirane Ring Opening

Polymer mechanochemistry induces chemical reactivity by applying a directed force, which can lead to unexpected reaction mechanisms. Strained cyclic molecules are often used in force-sensitive motifs because of the strong force coupling of ring-opening reactions. In this computational study, the force dependence of the ring-opening reactions of oxirane will be investigated. Density functional theory and multireference methods were used to investigate the electronic character of both symmetry-allowed and symmetry-forbidden reactions. In the latter case, an orbital crossing occurs during the reaction course, forcing the Woodward-Hoffmann-forbidden reaction to proceed via a diradical pathway. The performance of broken-symmetry density functional theory is evaluated and compares well to high-accuracy CASPT2, MRCI, and ic-MRCC computations. Due to the high ring strain, the barrier heights of both ring-opening reactions are steeply reduced by the application of an external force. Furthermore, the use of unsaturated linkers was shown to yield a significant reduction of the barrier heights, explaining previous experimental findings. Finally, we show through analysis of the PES topology how the external force transforms characteristic points such as saddle points and bifurcations, providing insights into force-dependent mechanism changes.

Probing the Electronic Manifold of MgCl with Millimeter-Wave Spectroscopy and Theory: (3)2Σ+ and (4)2Σ+ States

The millimeter/submillimeter spectrum of magnesium chloride (MgCl) has been observed in two new electronic excited states, (3)2Σ+ and (4)2Σ+, using direct absorption methods. The molecule was synthesized in a mixture of Cl2, argon, and magnesium vapor. For the (3)2Σ+ state, multiple rotational transitions were measured in the v = 0 level for all six isotopologues (24Mg35Cl, 24Mg37Cl, 25Mg35Cl, 25Mg37Cl, 26Mg35Cl, and 26Mg37Cl), as well as up to v = 13 for 24Mg35Cl. For the (4)2Σ+ state, less intense spectra were recorded for 24Mg35Cl (v = 0-2). Equilibrium rotational parameters were determined for both states for 24Mg35Cl, as well as rotational constants and 25Mg hyperfine parameters for the other isotopologues. A perturbation was observed between rotational levels of the two states due to an avoided crossing. Computations were also carried out at the CASPT2 and MRCISD+Q levels, and the resulting bond lengths for (3)2Σ+ and (4)2Σ+ states agree well with the experimental values of re = 2.536 and 2.361 Å. The computations show that the (3)2Σ+ state has a double-well potential; however, the state behaves as a single well with unperturbed vibrational levels up to v = 13 due to nonadiabatic interactions with the (4)2Σ+ state.

On the ground and excited electronic states of LaCO and AcCO

High-level ab initio electronic structure analysis of correlated lanthanide- and actinide-based species is laborious to perform and consequently limited in the literature. In the present work, the ground and electronically excited states of LaCO and AcCO molecules were explored utilizing the multireference configuration interaction (MRCI), Davidson corrected MRCI (MRCI+Q), and coupled cluster singles doubles and perturbative triples [CCSD(T)] quantum chemical tools conjoined with correlation consistent triple-ζ and quadruple-ζ quality all-electron Douglas-Kroll (DK) basis sets. The full potential energy curves (PECs), dissociation energies (Des), excitation energies (Tes), bond lengths (res), harmonic vibrational frequencies (ωes), and chemical bonding patterns of low-lying electronic states of LaCO and AcCO are introduced. The ground electronic state of LaCO is a 4Σ- (1σ11π2) which is a product of the reaction between excited La(4F) versus CO(X1Σ+), whereas the ground state of AcCO is a 12Π (1σ21π1) deriving from ground state fragments Ac(2D) + CO(X1Σ+). The spin-orbit ground states of LaCO (14Σ-3/2) and AcCO (12Π1/2) bear ∼13 and 5 kcal mol-1D0 values, respectively. At the MRCI level, the spin-orbit curves, the spin-orbit mixing, and the Tes of spin-orbit states of LaCO and AcCO were also analyzed. Lastly, the density functional theory (DFT) calculations were performed applying 16 exchange-correlation functionals that span three rungs of "Jacob's ladder" of density functional approximations (DFAs) to assess DFT errors associated on the De and ionization energy (IE) of LaCO.

Ab initio exploration of low-lying electronic states of linear and bent MNX+ (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) and their origins

High-level multireference and coupled cluster quantum calculations were employed to analyze low-lying electronic states of linear-MNX+ and side-bonded-M[NX]+ (M = Ca, Sr, Ba, Ra; X = O, S, Se, Te, Po) species. Their full potential energy curves (PECs), dissociation energies (Des), geometric parameters, excitation energies (Tes), and harmonic vibrational frequencies (ωes) are reported. The first three chemically bound electronic states of MNX+ and M[NX]+ are 3∑-, 1Δ, 1∑+ and 3A″, 1A', 1A″, respectively. The 3∑-, 1Δ, 1∑+ of MNX+ originate from the M+(2D) + NX(2Π) fragments, whereas the 3A″, 1A', 1A″ states of M[NX]+ dissociate to M+(2S) + NX(2Π) as a result of avoided crossings. The MNX+ and M[NX]+ are real minima on the potential energy surface and their interconversions are possible. The M2+NX-/M2+[NX]- ionic structure is an accurate representation for their low-lying electronic states. The Des of MNX+ species were found to depend on the dipole moment (μ) of the corresponding NX ligands and a linear relationship between these two parameters was observed.

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.

The Paradox of Global Multireference Diagnostics

Modern computational chemistry methods are a useful tool for modeling many chemical systems, but they are challenged by multireference species (e.g., transition metals). A variety of diagnostics have been formulated to identify such cases. They are typically developed by analyzing multireference characters of small molecules, and many provide an average picture of the entire system. We caution the use of such diagnostics for large systems because large systems may include parts with varying degrees of multireference characters. Specifically, a small but highly multireference component may yield a large error in absolute terms, which may be masked in an average value over the entire molecule. As the calculation of molecular relative energies often concerns errors in absolute terms, such a false sense of safety may be detrimental. A prospective means to tackle this challenge is to use fractional occupation density to identify potentially problematic components in a system and then examine this moiety with higher-level computations on appropriately constructed smaller models.

Improvement on the screening of nonlinear commutator operations in selective coupled-cluster using Lagrangian

We introduce a Lagrangian implementation of the full coupled-cluster reduction [Xu et al., Phys. Rev. Lett. 121, 113001 (2018)], that is, a selected coupled-cluster (CC) based on an arbitrary-order full CC expansion using direct commutator expansions. In this method, the screening for the products of cluster amplitudes plays a central role to reduce the computational cost for the nonlinear commutator operations, while the convergence of the total energy in the standard energy expression is not rapid with tightening the threshold. The new implementation using Lagrangian is robust, containing error only quadratic to those of amplitudes, allowing a much larger screening threshold. We demonstrate the performance of the new implementation by investigating the calculations of N2 and C6H6. The accuracy and applicability are also demonstrated for the potential energy curve of H2O in comparison with conventional quantum chemical methods.

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

In this paper, we investigate the role of electron correlation in predicting the S1-S0 and T1-S0 excitation energies and, hence, the singlet-triplet gap (ΔEST) in a set of cyclazines, which act as templates for potential candidates for fifth generation organic light emitting diode materials. This issue has recently garnered much interest with the focus being on the inversion of the ΔEST, although experiments have indicated near degenerate levels with both positive and negative being within the experimental error bar [J. Am. Chem. Soc. 102, 6068 (1980), J. Am. Chem. Soc. 108, 17(1986)]. We have carried out a systematic and exhaustive study of various excited state electronic structure methodologies and identified the strengths and shortcomings of the various approaches and approximations in view of this challenging case. We have found that near degeneracy can be achieved either with a proper balance of static and dynamic correlation in multireference theories or with state-specific orbital corrections, including its coupling with correlation. The role of spin contamination is also discussed. Eventually, this paper seeks to produce benchmark numbers for establishing cost-effective theories, which can then be used for screening derivatives of these templates with desirable optical and structural properties. Additionally, we would like to point out that the use of domain-based local pair natural orbital-similarity transformed EOM-coupled cluster singles and doubles as the benchmark for ΔEST [as used in J. Phys. Chem. A 126(8), 1378 (2022), Chem. Phys. Lett. 779, 138827 (2021)] is not a suitable benchmark for these classes of molecules.

Ground and Excited Electronic Structure Analysis of FeH with Correlated Wave Function Theory and Density Functional Approximations

FeH is one of the most challenging diatomic molecules to study under electronic structure theory. Here, we have successfully studied 22 electronic states of FeH using ab initio multireference configuration interaction (MRCI), Davidson-corrected MRCI (MRCI+Q), and coupled cluster singles, doubles, and perturbative triples [CCSD(T)] levels of theory. We report their potential energy curves (PECs), excitation energies, dissociation energies, equilibrium electronic configurations, and a series of spectroscopic constants with the use of augmented triple-ζ, quadruple-ζ, and quintuple-ζ quality correlation consistent basis sets. The scalar relativistic effects and active space and core electron correlation contribution on the properties of FeH are also explored. The use of a large CASSCF active space that includes 4s, 4p, 3d, and 4d orbitals of Fe and the 1s of H is critical for producing accurate full PECs with proper dissociations and predicting the exact order of the electronic states. Our findings are in harmony with the experimental results available in the literature and will serve as reference values for future studies of FeH. Furthermore, with the use of PECs, the total internal partition function sum (TIPS) of FeH was calculated across a range of temperatures. Finally, we exploited the single-reference nature of the a6Δ of FeH and its ionized product FeH+ (X5Δ) to evaluate the associated density functional theory (DFT) errors on their dissociation energies and spectroscopic parameters.

Semiclassical Nonadiabatic Molecular Dynamics Using Linearized Pair-Density Functional Theory

Nonadiabatic molecular dynamics is an effective method for modeling nonradiative decay in electronically excited molecules. Its accuracy depends strongly on the quality of the potential energy surfaces, and its affordability for long direct-dynamic simulations with adequate ensemble averaging depends strongly on the cost of the required electronic structure calculations. Linearized pair-density functional theory (L-PDFT) is a recently developed post-self-consistent-field multireference method that can model potential energy surfaces with an accuracy similar to expensive multireference perturbation theories but at a computational cost similar to the underlying multiconfiguration self-consistent field method. Here, we integrate the SHARC dynamics and PySCF electronic structure code to utilize L-PDFT for electronically nonadiabatic calculations and use the combined programs to study the photoisomerization reaction of cis-azomethane. We show that L-PDFT is able to successfully simulate the photoisomerization without crashes, and it yields results similar to the more expensive extended multistate complete active space second-order perturbation theory. This shows that L-PDFT can model internal conversion, and it demonstrates its promise for broader photodynamics applications.

Ab Initio Neural Network Potential Energy Surface and Quantum Dynamics Calculations on Na(2S) + H2 → NaH + H Reaction

The collisions between Na atoms and H2 molecules are of great significance in the field of chemical reaction dynamics, but the corresponding dynamics results of ground-state reactions have not been reported experimentally or theoretically. Herein, a global and high-precision potential energy surface (PES) of NaH2 (12A') is constructed by the neural network model based on 21,873 high-level ab initio points. On the newly constructed PES, the quantum dynamics calculations on the Na(2S) + H2(v0 = 0, j0 = 0) → NaH + H reaction are carried out using the time-dependent wave packet method to study the microscopic reaction mechanism at the state-to-state level. The calculated results show that the low-vibrational products are mainly formed by the dissociation of the triatomic complex; whereas, the direct reaction process dominates the generation of the products with high-vibrational states. The reaction generally follows the direct H-abstraction process, and there is also the short-lived complex-forming mechanism that occurs when the collision energy exceeds the reaction threshold slightly. The PES could be used to further study the stereodynamics effects of isotope substitution and rovibrational excitations on the title reaction, and the presented dynamics data would provide an important reference on the corresponding experimental research at a higher level.

Low temperature dynamics of H + HeH+→ H2+ + He reaction: On the importance of long-range interaction

While the growing realization of the importance of long-range interactions is being demonstrated in cold and ultracold bimolecular collision experiments, their influence on one of the most critical ion-neutral reactions has been overlooked. Here, we address the non-Langevin abrupt decrease observed earlier in the low-energy integral cross-sections and rate coefficients of the astrochemically important H + HeH+→ H2+ + He reaction. We attribute this to the presence of artificial barriers on existing potential energy surfaces (PESs). By incorporating precise long-range interaction terms, we introduce a new refined barrierless PES for the electronic ground state of HeH2+ reactive system, aligning closely with high-level ab initio electronic energies. Our findings, supported by various classical, quantum, and statistical methods, underscore the significance of long-range terms in accurately modeling reactive PESs. The low-temperature rate coefficient on this new PES shows a substantial enhancement as compared to the previous results and aligns with the Langevin behavior. This enhancement could noticeably affect the prediction of HeH+ abundance in early Universe condition.

Complete Active Space Iterative Coupled Cluster Theory

In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected CC. This is accomplished by establishing a feedback loop between the CC and CAS parts of a calculation through a similarity transformation of the Hamiltonian with those CC amplitudes that are not encompassed by the active space. We denote this approach as the complete active space iterative coupled cluster (CASiCC) ansatz. We investigate its efficiency and accuracy in the singles and doubles approximation by studying the prototypical molecules H4, H8, H2O, and N2. Our results demonstrate that CASiCC systematically improves on the single-reference CCSD and the externally corrected CCSD methods across entire potential energy curves while retaining modest computational costs. However, the tailored coupled cluster method shows superior performance in the strong correlation regime, suggesting that its accuracy is based on error compensation. We find that the iterative versions of externally corrected and tailored coupled cluster methods converge to the same results.

Reconciling Accuracy and Feasibility for Barrierless Reaction Steps by the PCS/DDCI/MC-PDFT Protocol: Methane and Ethylene Dissociations as Case Studies

Several enhancements have been introduced into state-of-the-art computational protocols for the treatment of barrierless reaction steps in the framework of variable reaction coordinate variational transition state theory. The first step is the synergistic integration of the Iterative Difference Dedicated Configuration Interaction (I-DDCI) and Pisa Composite Scheme, which defines a reduced cost, yet very accurate, computational workflow. This approach provides a near black box tool for obtaining 1D reference potentials. Then, a general strategy has been devised for tuning the level of theory used in Monte Carlo (MC) sampling, employing Multiconfiguration Pair Density Functional Theory (MC-PDFT) with dynamically adjusted Hartree-Fock exchange. Concurrently, partial geometry optimizations during the MC simulations account for the coupling between the reaction coordinates and conserved modes. The protocol closely approaches full size consistency and yields highly accurate results, with several test computations suggesting rapid convergence of the I-DDCI correction with the basis set dimensions. The capabilities of the new platform are illustrated by two case studies (the hydrogen dissociation from CH4 and C2H4), which highlight its flexibility in handling different carbon hybridizations (sp3 and sp2). The remarkable accuracy of the computed rate constants confirms the robustness of the proposed method. Together with their intrinsic interest, these results pave the way for systematic investigations of complex gas-phase reactions through a reliable, user-friendly tool accessible to specialists and nonspecialists alike.