CASSCF Research Articles

Fully Polarizable Multiconfigurational Self-Consistent Field/Fluctuating Charges Approach.

A multiscale model based on the coupling of the multiconfigurational self-consistent field (MCSCF) method and the classical atomistic polarizable fluctuating charges (FQ) force field is presented. The resulting MCSCF/FQ approach is validated by exploiting the CASSCF scheme through application to compute vertical excitation energies of formaldehyde and para-nitroaniline in aqueous solution. The procedure is integrated with molecular dynamics simulations to capture the solute's conformational changes and the dynamic aspects of solvation. Comparative analysis with alternative solvent models, gas-phase calculations, and experimental data provides insights into the model's accuracy in reproducing solute-solvent molecular interactions and spectral signals.

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.

Hollow ion atomic structure and X-ray emission in dense hot plasmas

Hollow ion X-ray emission is of great interest in high-energy-density research, since negligible opacity allows studies from the interior of very dense objects. In this paper, ionization potential depressions of the isoelectronic sequences for single and double K-shell vacancies are obtained from a pure ab initio multiconfiguration Hartree–Fock simulation including exact exchange terms and finite temperature dense plasma effects. It is demonstrated that the simultaneous representation of these ab initio data in the form of a map of hollow ion X-ray transition energies enables identification of important steps in the matter evolution and ionization dynamics. Mapping along the isoelectronic sequence as a function of the pumping energy of a X-ray free electron laser also enables visualization of the impact of ionization potential depression on the pathways of hollow ion formation.

Ionic Fragmentation of the Halothane Molecule Induced by EUV and Soft X-ray Radiation.

EUV and soft X-ray-induced photofragmentation of the halothane (CF3CHBrCl) molecule has been investigated using time-of-flight mass spectrometry in the coincidence mode (PEPICO) covering the valence region and vicinity of the bromine 3d, chlorine 2p, and carbon 1s edges. Total and partial ion yields have been recorded as a function of photon energy. At lower photon energies, the heavier singly charged molecular fragments predominate in the mass spectra. On the other hand, there is a strong tendency to the atomization of the molecule at higher photon energies. Despite the different chemical environments experienced by the two carbon atoms, weak site-specific fragmentation is observed. In addition, ab initio quantum mechanical calculations at the MP2 level and a series of computations with multiconfigurational self-consistent field have been performed to describe the inner-shell states.

Amesp: Atomic and molecular electronic structure program

The atomic and molecular electronic structure program (Amesp) is a general-purpose electronic structure program designed for the study of molecular electronic structures. It incorporates a series of modern electronic structure methods, including Hartree–Fock, density functional theory, Multiconfigurational self-consistent field, Møller–Plesset, configuration-interaction, coupled-cluster, semiempirical methods, and molecular force fields. Amesp strives to offer an efficient and user-friendly tool specifically designed for computing for molecules ranging from small to complex biomolecules. In this paper, we highlight the features of Amesp and offer an overview.

Which Options Exist for NISQ-Friendly Linear Response Formulations?

Linear response (LR) theory is a powerful tool in classic quantum chemistry crucial to understanding photoinduced processes in chemistry and biology. However, performing simulations for large systems and in the case of strong electron correlation remains challenging. Quantum computers are poised to facilitate the simulation of such systems, and recently, a quantum linear response formulation (qLR) was introduced [Kumar et al., J. Chem. Theory Comput. 2023, 19, 9136-9150]. To apply qLR to near-term quantum computers beyond a minimal basis set, we here introduce a resource-efficient qLR theory, using a truncated active-space version of the multiconfigurational self-consistent field LR ansatz. Therein, we investigate eight different near-term qLR formalisms that utilize novel operator transformations that allow the qLR equations to be performed on near-term hardware. Simulating excited state potential energy curves and absorption spectra for various test cases, we identify two promising candidates, dubbed "proj LRSD" and "all-proj LRSD".

Prediction Challenge: Simulating Rydberg photoexcited cyclobutanone with surface hopping dynamics based on different electronic structure methods.

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n → 3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction [multiconfigurational self-consistent field (MCSCF)] specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10ps), followed by an ultrafast population transfer from S1 to S0 (<100fs). CO elimination (C3 channel) dominates over C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10-250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics.

Potential-Energy Curves for the Ground and Several Electronic States of NdO and NdS.

Potential energy curves (PECs) were calculated for 21 and 18 electronic states of NdO and NdS molecules, respectively. In each case, static electron correlation effects were described by incomplete model space multiconfiguration self-consistent field wave functions based on an active space that included the most important valence orbitals. Dynamic electron correlation was included by the multireference second-order generalized Van Vleck perturbation theory method. Scalar-relativistic contributions were included by the effective core potential approach, using def2-TZVPP basis sets. Spin-dependent relativistic corrections were determined to be small and negligible for the Nd atom and so were not included in the calculations. The 21 and 18 electronic states of NdO and NdS were predicted to be in the excitation energy range of ∼3.2 and ∼2.7 eV, respectively. The ground electronic states of NdO and NdS were determined as 15H (6s4fσ4fϕ4fδ) and 15H (4fϕ4fπ4fπ6s), with spectroscopic constants: bond length Re = 1.780 and 2.325 Å, and harmonic frequency ωe = 891 and 538 cm-1, respectively.

Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density.

Lagrangians of the state-averaged multiconfigurational self-consistent field (SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density are defined. In addition, variational equations were derived to calculate the excitation energies of the target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions, and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines, including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role in predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12000 basis functions.

Unveiling the quantum secrets of triel metal triangles: a tale of stability, aromaticity, and relativistic effects.

Low lying electronic states of Al3-, Ga3-, In3-, and Tl3- have been characterized using high level multiconfigurational quasi degenerate perturbation theory on the multiconfigurational self-consistent field. Among these species, the singlet states emerge as the predominant energy minima, displaying remarkable stability. However, within the Tl3- series, our investigation leads to the identification of the high-spin , as the most stable spin state, a result corroborated by previous experimental detection via photoelectron spectroscopy. Similarly, we have also identified the singlet state of In3- as the signal detected previously experimentally. By applying Mandado's rules and an array of aromaticity indicators, it is conclusively demonstrated that both the singlet and quintet states exhibit multiple-fold aromaticity, while the triplets exhibit conflicting aromaticity. Furthermore, this investigation highlights the significant impact of relativistic effects, as they enhance the stability of the state relative to its singlet counterpart. These findings shed new light on the electronic structures and properties of these ions, offering valuable insights into their chemical behavior and potential applications.

Unravelling the electronic structure, bonding, and magnetic properties of inorganic dysprosocene analogues [Dy(E4)2]- (E = N, P, As, CH).

Organometallic sandwich complexes of Dy(III) ion are ubiquitous for designing high-temperature single-ion magnets with blocking temperatures close to the liquid nitrogen boiling point. Magnetic bistability at the molecular level makes them potential candidates for nano-scale information storage materials. In the present contribution, we have thoroughly investigated the electronic structure, bonding, covalency, and magnetic anisotropy of inorganic dysprosocene complexes with a general formula of [Dy(E4)2]- (where E = N, P, As, CH) using state-of-the-art scalar relativistic density functional theory (SR-DFT), and a multiconfigurational complete active space self-consistent field (CASSCF) method with the N-electron valence perturbation theory (NEVPT2). Geometry optimization calculations predict stabilization of the [Dy(E4)2]- complexes with a linear geometry and D4h local symmetry Dy(III) ion in [Dy(N4)2]- (1) and [Dy(P4)2]- (2) complexes, while a bent geometry has been observed for the [Dy(As4)2]- (3), [Dy(P2(CH)2)2]- (4), and [Dy(As2(CH)2)2]- (5) complexes. Energy decomposition analysis (EDA) and natural bonding orbital (NBO) calculations reveal sizable 5d-ligand covalency followed by 6s/6p and weak 4f-ligand covalency in complexes 1-5. Both the natural localized molecular orbitals (NLMOs) at the DFT level and ab initio-based ligand field theory (AILFT) at the NEVPT2 level of theory predict an increase in the Dy-ligand covalency as we move from N to As. Spin-Hamiltonian parameter analysis of complexes 1-5 reveals stabilization of the mJ |±15/2〉 as the ground state with highly axial g values (gxx ∼ gyy ∼ 0 and gzz ∼ 20) and the barrier height of 2902, 1214, 1104, 1845, and 1509 K for 1-5, respectively. The Orbach effective demagnetization barrier (Ueff) for complexes 1-5 ranges between 2416-1175 K, with a record Ueff value of 2416 K observed for 1. In addition, we have explored the role of heavy element effects on the magnetic anisotropy by turning off the spin-orbit coupling of the pnictogens (N, P, and As), and our calculations clearly predict that heavy atoms in the first coordination sphere help in increasing the barrier height for magnetic relaxation. Heavy elements like P and As significantly enhance the SOC contributions, thereby providing a platform for designing and optimizing Dy(III) complexes with tailored magnetic behaviors.

Linear Response Equations Revisited: A Simple and Efficient Iterative Algorithm.

We present an algorithm to solve the linear response equations for Hartree-Fock, Density Functional Theory, and the Multiconfigurational Self-Consistent Field method that is both simple and efficient. The algorithm makes use of the well-established symmetric and antisymmetric combinations of trial vectors but further orthogonalizes them with respect to the scalar product induced by the response matrix. This leads to a standard, symmetric block eigenvalue problem in the expansion subspace that can be solved by diagonalizing a symmetric, positive definite matrix half the size of the expansion space. Numerical tests showed that the algorithm is robust and stable.

How Axial Coordination Regulates the Electronic Structure and C-H Amination Reactivity of Fe-Porphyrin-Nitrene?

Detailed electronic structure and its correlation with the intramolecular C-H amination reactivity of Fe-porphyrin-nitrene intermediates bearing different "axial" coordination have been investigated using multiconfigurational complete active space self-consistent field (CASSCF), N-electron valence perturbation theory (NEVPT2), and hybrid density functional theory (DFT-B3LYP) calculations. Three types of "axial" coordination, -OMe/-O(H)Me (1-Sul/2-Sul), -SMe/-S(H)Me (3-Sul/4-Sul), and -NMeIm (MeIm = 3-methyl-imidazole) (5-Sul) mimicking serine, cysteine, and histidine, respectively, along with no axial coordination (6-Sul) have been considered to decipher how the "axial" coordination of different strengths regulates the electronic integrity of the Fe-N core and nitrene-transfer reactivity of Fe-porphyrin-nitrene intermediates. CASSCF-based natural orbitals reveal two distinct classes of electronic structures: Fe-nitrenes (1-Sul and 3-Sul) with relatively stronger axial coordination (-OMe and -SMe) display "imidyl" nature and those (2-Sul, 4-Sul, and 6-Sul) with weaker axial coordination (-O(H)Me, -S(H)Me and no axial coordination) exhibit "imido-like" character. A borderline between the two classes is also observed with NMeIm axial coordination (5-Sul). Axial coordination of different strengths not only regulates the electronic structure but also modulates the Fe-3d orbital energies, as revealed through the d-d transition energies obtained by CASSCF/NEVPT2 calculations. The relatively lower energy of Fe-3dz2 orbital allows easy access to low-lying high-spin quintet states in the cases of weaker "axial" coordination (2-Sul, 4-Sul, and 6-Sul), and the associated hydrogen atom transfer (HAT) reactivity appears to involve two-state triplet-quintet reactivity through minimum energy crossing point (3,5MECP) between the spin states. In stark contrast, Fe-nitrenes with relatively stronger "axial" coordination (1-Sul and 3-Sul) undergo triplet-only HAT reactivity. Overall, this in-depth electronic structure investigation and HAT reactivity evaluation reveal that the weaker axial coordination in Fe-porphyrin-nitrene complexes (2-Sul, 4-Sul, and 6-Sul) can promote more efficient C-H oxidation through the quintet spin state.

The Co-N bond cleavage in the adenosyncobalamin cofactor in advance to glutamate mutase and methylmalonyl-CoA mutase processes

The in vivo experiments show that the adenosylcobalamin cofactor in glutamate mutase and methylmalonyl-CoA mutase processes lose its dimethylbenzimidazole axial ligand before starting the enzymatic processes. Complete active space self-consistent field geometry optimization of the vitamin B12 active forms plus substrates joint models have been performed. These joint models include the adenosylcobalamin cofactor, the carboxyl negative ion model of the studied processes’ active substrates, and the histidine molecule. Partial electronic density is transferred from the highest occupied substrate molecular orbitals to the lowest unoccupied antibonding molecular orbitals, which consist of corrin ring and dimethylbenzimidazole ligand common molecular orbitals during the multi-configurational self-consistent field molecular orbital mixing process. As a result, the Co-N axial bond is permanently elongated during the complete active space self-consistent field geometry optimization until its complete rupture and until the removal of the dimethylbenzimidazole ligand from the central cobalt atom and the corrin ring is complete. The Co-N bond cleavage in the adenosylcobalamin cofactors in the studied processes is running as no energy barrier process under the influence of their active substrates and histidine molecule.

Rotational Transitions in the N2 + Ion Induced by Collisions with Helium Atoms in Cold Helium Plasmas. A Quasiclassical Trajectory Study.

Cross-sections of state-to-state rotational transitions in electronically ground-state 14 (X2 ) ions induced by collisions with 4 He atoms have been calculated using a quasiclassical trajectory method and a set of artificial neural networks representing the /He potential energy surface. The training points for the neural networks have been calculated at a MCSCF (multi-configuration self-consistent field)/aug-cc-pVQZ level. A broad range of the /He collision energy has been considered ( eV) and the efficiency of vibrational transitions in the ion has also been analyzed. It has been found that vibrational transitions are negligible with respect to rotational transitions up to eV and that above this energy, both rotational and vibrational transitions in are marginal in the /He collisions.

Vibrational and Dipolar Calculations of Mg-(Li, Na, K) Polar Molecules

In this present paper, high-level ab-initio calculations were well performed using multi-configuration self-consistent field, multi-reference configuration interaction and pseudo-potentials methods of diatomic polar molecules compound to magnesium and an alkali atom (Li, Na, K) essentially for the ground and different low-lying excited electronic states of both symmetries 2,4Σ+ and 2,4Π. In this context, adiabatic potential energy curves have been carefully derived as well as the spectroscopic parameters for the different states correlated up to {Mg (3s2)+Li (4 s)}, {Mg (3s2)+Na (4p)} and {Mg (3s2)+K (4d)} asymptotic limits for the studied systems. The obtained results are discussed and compared with the previous theoretical and experimental works which feature in general a good agreement. Afterward, vibrational levels and their spacings as well as the permanent and transition dipole moment curves were accurately calculated. Finally, the turning points (intersection of the potential energy curve with the considered vibrational levels) as well as the ro-vibrational parameter (Bv), were determined for the ground (X)2Σ+ and the first excited state (2)2Σ+. Thanks to their strong dipole-dipole interaction as well as their long coherence time, some bibliographical review have affirmed that these molecular systems can be considered firstly as perfect potential carriers for information in the field of molecular quantum computing and secondly as very promising candidates for certain experiments such as photo-association and laser cooling.

Potential energy curves of molecular nitrogen up to N

The potential energy curves for molecular ions up to N are calculated in an ab initio manner using the multi configurational self-consistent field method. Specifically, we implement in an automatic way a previously used double loop optimisation scheme within the multi configurational self-consisted field method. We obtain the potential energy curves up to N ions with any combination of core, inner valence, and outer valence holes. Finally, we provide the code used to generate these potential energy curves.

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment.

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed.

Understanding the Excited-State Relaxation Mechanisms of Xanthophyll Lutein by Multi-configurational Electronic Structure Calculations.

The contradictory behaviors in light harvesting and non-photochemical quenching make xanthophyll lutein the most attractive functional molecule in photosynthesis. Despite several theoretical simulations on the spectral properties and excited-state dynamics, the atomic-level photophysical mechanisms need to be further studied and established, especially for an accurate description of geometric and electronic structures of conical intersections for the lowest several electronic states of lutein. In the present work, semiempirical OM2/MRCI and multi-configurational restricted active space self-consistent field methods were performed to optimize the minima and conical intersections in and between the 1Ag-, 2Ag-, 1Bu+, and 1Bu- states. Meanwhile, the relative energies were refined by MS-CASPT2(10,8)/6-31G*, which can reproduce correct electronic state properties as those in the spectroscopic experiments. Based on the above calculation results, we proposed a possible excited-state relaxation mechanism for lutein from its initially populated 1Bu+ state. Once excited to the optically bright 1Bu+ state, the system will propagate along the key reaction coordinate, i.e., the stretching vibration of the conjugated carbon chain. During this period of time, the 1Bu- state will participate in and forms a resonance state between the 1Bu- and 1Bu+ states. Later, the system will rapidly hop to the 2Ag- state via the 1Bu+/2Ag- conical intersection. Finally, the lutein molecule will survive in the 2Ag- state for a relatively long time before it internally converts to the ground state directly or via a twisted S1/S0 conical intersection. Notably, though the photophysical picture may be very different in solvents and proteins, the current theoretical study proposed a promising calculation protocol and also provided many valuable mechanistic insights for lutein and similar carotenoids.