Multiconfigurational Perturbation Theory Research Articles

Knowles Partitioning at the Multireference Level.

A multireference generalization of the partitioning introduced recently by Knowles (J. Chem. Phys. 2022 156, 011101) is presented with the aim to study electronic systems at a medium level of correlation. The multireference formalism applied is the general framework of multiconfiguration perturbation theory (MCPT).

Anisole-Water and Anisole-Ammonia Complexes in Ground and Excited (S1) States: A Multiconfigurational Symmetry-Adapted Perturbation Theory (SAPT) Study.

Binary complexes of anisole have long been considered paradigm systems for studying microsolvation in both the ground and electronically excited states. We report a symmetry-adapted perturbation theory (SAPT) analysis of intermolecular interactions in anisole-water and anisole-ammonia complexes within the framework of the multireference SAPT(CAS) method. Upon the S1 ← S0 electronic transition, the hydrogen bond in the anisole-water dimer is weakened, which SAPT(CAS) shows to be determined by changes in the electrostatic energy. As a result, the water complex becomes less stable in the relaxed S1 state despite decreased Pauli repulsion. Stronger binding of the anisole-ammonia complex following electronic excitation is more nuanced and results from counteracting shifts in the repulsive (exchange) and attractive (electrostatic, induction and dispersion) forces. In particular, we show that the formation of additional binding N-H···π contacts in the relaxed S1 geometry is possible due to reduced Pauli repulsion in the excited state. The SAPT(CAS) interaction energies have been validated against the coupled cluster (CC) results and experimentally determined shifts of the S1 ← S0 anisole band. While for the hydrogen-bonded anisole-water dimer SAPT(CAS) and CC shifts are in excellent agreement, for ammonia SAPT(CAS) is only qualitatively correct.

Photoionization of aziridine: Nonadiabatic dynamics of the first six low-lying electronic states of the aziridine radical cation.

In this article, the theoretical photoionization spectroscopy of the aziridine (C2H5N) molecule is investigated. To start with, we have optimized the geometry of this molecule at the neutral electronic ground state at the density functional theory/augmented correlation-consistent polarized valence triple zeta level of theory using the G09 program. The electronic structure calculations were restricted to the first six low-lying electronic states in order to account for the experimental photoelectron spectrum of the C2H5N molecule. The first six low-lying electronic states (X̃2A', Ã2A', B̃2A″, C̃2A″, D̃2A', and Ẽ2A') of the potential energy surfaces (PESs) are calculated by both equation of motion-ionization potential-coupled cluster singles and doubles and multi-configuration quasi-degenerate perturbation theory abinitio quantum chemistry methods along the dimensionless normal displacement coordinates in which multiple conical intersections were established among the considered electronic states. A (6 × 6) model vibronic Hamiltonian is constructed on a diabatic electronic basis, using the symmetry selection rules and Taylor series expansion. The Cs symmetry point group of the aziridine molecule leads to electronic states symmetry of either A' or A″, and these states are close in energy, due to which the same symmetry electronic states avoid each other. To get a smooth diabatic PES, a fourfold diabatization scheme is used, which is implemented in the General Atomic and Molecular Electronic Structure Systems suite of programs. All the parameters used in the diabatic vibronic coupling model Hamiltonian are calculated in terms of the normal modes of vibrational coordinates. Finally, the vibronic model Hamiltonian constructed for the coupled six electronic states is used to solve both time-independent and time-dependent Schrödinger equations using the multi-configuration time-dependent Hartree program module to obtain the dynamical observables. The theoretical vibronic band structure is found to be in good accord with the available experimental results.

Electronic and vibrational spectroscopy of benzonitrile cation for astrochemical consideration.

The electronic and vibrational spectra of benzonitrile cation, C6H5CN+ (BZN+), in the gas phase at low temperatures are reported. Measurements were carried out using a cryogenic ion trapping apparatus. The mid-infrared spectrum shows a strong CN stretch at 2130 ± 1 cm-1 (4.694 ± 0.002 µm). The electronic spectrum is reported in the range 5040-5750Å. This covers the forbidden B2B2 ← X2B1 and allowed C2B1 ← X2B1 transitions. The spectrum is dominated by a broad absorption feature at wavelengths shorter than 5250Å, with the strongest absorption located at 5140Å. Experimental data are complemented with quantum chemical calculations carried out at the density functional theory and extended multi-configurational quasi-degenerate perturbation theory level. The spectroscopic results are discussed in the context of astronomical observations in the infrared and visible.

ExROPPP: Fast, accurate, and spin-pure calculation of the electronically excited states of organic hydrocarbon radicals.

Recent years have seen an explosion of interest in organic radicals due to their promise for highly efficient organic light-emitting diodes and molecular qubits. However, accurately and inexpensively computing their electronic structure has been challenging, especially for excited states, due to the spin-contamination problem. Furthermore, while alternacy or "pseudoparity" rules have guided the interpretation and prediction of the excited states of closed-shell hydrocarbons since the 1950s, similar general rules for hydrocarbon radicals have not to our knowledge been found yet. In this article, we present solutions to both of these challenges. First, we combine the extended configuration interaction singles method with Pariser-Parr-Pople (PPP) theory to obtain a method that we call ExROPPP (Extended Restricted Open-shell PPP) theory. We find that ExROPPP computes spin-pure excited states of hydrocarbon radicals with comparable accuracy to experiment as high-level general multi-configurational quasi-degenerate perturbation theory calculations but at a computational cost that is at least two orders of magnitude lower. We then use ExROPPP to derive widely applicable rules for the spectra of alternant hydrocarbon radicals, which are completely consistent with our computed results. These findings pave the way for highly accurate and efficient computation and prediction of the excited states of organic radicals.

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.

Assessment of DFT functionals for a minimal nitrogenase [Fe(SH)4H]- model employing state-of-the-art abinitio methods.

We have designed a [Fe(SH)4H]- model with the fifth proton binding either to Fe or S. We show that the energy difference between these two isomers (∆E) is hard to estimate with quantum-mechanical (QM) methods. For example, different density functional theory (DFT) methods give ∆E estimates that vary by almost 140 kJ/mol, mainly depending on the amount of exact Hartree-Fock included (0%-54%). The model is so small that it can be treated by many high-level QM methods, including coupled-cluster (CC) and multiconfigurational perturbation theory approaches. With extrapolated CC series (up to fully connected coupled-cluster calculations with singles, doubles, and triples) and semistochastic heat-bath configuration interaction methods, we obtain results that seem to be converged to full configuration interaction results within 5 kJ/mol. Our best result for ∆E is 101 kJ/mol. With this reference, we show that M06 and B3LYP-D3 give the best results among 35 DFT methods tested for this system. Brueckner doubles coupled cluster with perturbaitve triples seems to be the most accurate coupled-cluster approach with approximate triples. CCSD(T) with Kohn-Sham orbitals gives results within 4-11 kJ/mol of the extrapolated CC results, depending on the DFT method. Single-reference CC calculations seem to be reasonably accurate (giving an error of ∼5 kJ/mol compared to multireference methods), even if the D1 diagnostic is quite high (0.25) for one of the two isomers.

Valence and Core Photoelectron Spectra of Aqueous I3- from Multi-Reference Quantum Chemistry.

The I3- molecule is known to undergo substantial structural reorganization upon solvation by a protic solvent, e.g., water. However, the details of this process are still controversially discussed in the literature. In the present study, we combined experimental and theoretical efforts to disentangle this controversy. The valence (5p), N4,5 (4d), and M4,5 (3d) edge photoelectron spectra were measured in an aqueous solution and computed using high-level multi-reference methods. Our previous publication mainly focused on obtaining reliable experimental evidence, whereas in the present article, we focused primarily on theoretical aspects. The complex electronic structure of I3- requires the inclusion of both static and dynamic correlation, e.g., via the multi-configurational perturbation theory treatment. However, the resulting photoelectron spectra appear to be very sensitive to problems with variational stability and intruder states. We attempted to obtain artifact-free spectra, allowing for a more reliable interpretation of experiments. Finally, we concluded that the 3d Photoelectron Spectrum (PES) is particularly informative, evidencing an almost linear structure with a smaller degree of bond asymmetry than previously reported.

Mechanistic Understanding and Reactivity Analyses for the Photochemistry of Disubstituted Tetrazoles

The photolysis of tetrazoles has undergone extensive research. However, there are still some problems to be solved in terms of mechanistic understanding and reactivity analyses, which leaves room for theoretical calculations. Herein, multiconfiguration perturbation theory at the CASPT2//CASSCF level was employed to account for electron correction effects involved in the photolysis of four disubstituted tetrazoles. Based on calculations of vertical excitation properties and evaluations of intersystem crossing (ISC) efficiencies in the Frank-Condon region, the combination of space and electronic effects is found in maximum-absorption excitation. Two types of ISC (1ππ* → 3nπ*, 1ππ* → 3ππ*) are determined in disubstituted tetrazoles, and the obtained rates follow the El-Sayed rule. Through mapping three representative types of minimum energy profiles for the photolysis of 1,5-, and 2,5-disubstituted tetrazoles, a conclusion can be drawn that the photolysis of tetrazoles exhibits reactivity characteristic of bond-breaking selectivity. Kinetic evaluations show that the photogeneration of singlet imidoylnitrene operates predominately over that in the triplet state, which can be confirmed by a double-well model in the triplet potential energy surface of 1,5-disubstituted tetrazole. Similar mechanistic explorations and reactivity analyses were also applied to the photolysis of 2,5-disubstituted tetrazole to unveil fragmentation patterns of nitrile imine generation. All computational efforts allow us to better understand the photoreactions of disubstituted tetrazoles and to provide useful strategies for regulating their unique reactivity.

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.

Calculating Vertical Ionization Energies of Hydrated Biological Chromophores Based on Multiconfigurational Perturbation Theory

Here we introduce a methodology for calculating vertical detachment energies (VDE) and vertical ionization energies (VIE) of anionic and neutral chromophores in aqueous environment. The proposed method is based on the extended multiconfigurational quasidegenerate perturbation theory coupled to the explicit treatment of solvent effects in the frame of the effective fragment potential method. We show that the solvent polarization contribution must be considered for getting accurate quantitative estimations of VDEs and VIEs. The calculated values of VDE for phenolate (7.3 eV) and VIE for phenol (7.9 eV) in aqueous environment are in good agreement with the experimental results obtained using X-ray and multiphoton UV photoelectron spectroscopy. Our approach will be useful for studying processes of photoinduced electron transfer from anionic as well as neutral biological chromophores in aqueous solution.

Ultrafast Photoelimination of Nitrogen from Upper Excited States of Diazoalkanes and the Fate of Carbenes Formed in the Reaction

The photochemical reactivity of diphenyldiazomethane 1 and phenyl 1- and 2-adamantyl diazomethanes 2 and 3, respectively, was investigated by transient absorption spectroscopy (TA). Photoelimination of N2 upon UV excitation takes place in the anti-Kasha ultrafast photochemical reaction from the upper excited singlet states to deliver singlet carbenes, which were, in the case of 1 and 2, detected by fs-TA. The reactivity of the carbenes differs with respect to the substituent at the carbene center. The singlet car-1 in a nonpolar solvent delivers the triplet carbene by intersystem crossing (ISC). Singlet car-2 does not undergo ISC but reacts in the intermolecular insertion reactions into C-H bonds. Car-3 has an α-C-H bond next to the carbene center and reacts rapidly in the intramolecular C-H insertion reaction to deliver alkene, precluding its detection by fs-TA. However, the isolation of ketone photoproducts from 3 is highly indicative of triplet car-3's intermediate formation. The TA spectra from the S1-S3 states of 1-3 were computed using time-dependent density functional theory, while the multiconfigurational perturbation theory to the second order was used for the absorption spectra of the corresponding singlet and triplet carbenes. The modeled and measured spectra are in good agreement, and the computations corroborate the assignments of the key short-lived intermediates.

Pivot invariance of multiconfiguration perturbation theory via frame vectors.

Multiconfiguration perturbation theory (MCPT) is a general framework for correcting the reference function of arbitrary structures. The variants of MCPT introduced so far differ in the specification of their zero-order Hamiltonian, i.e., the partitioning. A common characteristic of MCPT variants is that no numerical procedure is invoked when handling the overlap of the reference function and determinants spanning the configuration space. This comes at the price of pinpointing a principal term in the determinant expansion of the reference, rendering the PT results dependent on this choice. It is here shown that the pivot dependence of MCPT can be eliminated by using an overcomplete set of projected determinants in the space orthogonal and complementary to the reference. The projected determinants form a so-called frame, a generalization of the notion of basis, allowing for redundancy of the set. The simple structure of the frame overlap matrix facilitates overlap treatment in closed form, a feature shared by previous MCPT variants. In particular, the Moore-Penrose inverse of singular matrices appearing in frame-based MCPT can be constructed without the need for any pivoting algorithm or numerical zero threshold. Pilot numerical studies are performed for the singlet-triplet gap of biradicaloid systems, relying on geminal-based, incomplete model space reference function. Comparison with previous MCPT variants as well as illustration of pivot invariance is provided.

Electronic states and transitions of PrO and PrO+ probed by threshold ionization spectroscopy and spin-orbit multiconfiguration perturbation theory.

The precise ionization energy of praseodymium oxide (PrO) seeded in supersonic molecular beams is measured with mass-analyzed threshold ionization (MATI) spectroscopy. A total of 33 spin-orbit (SO) states of PrO and 23 SO states of PrO+ are predicted by second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Electronic transitions from four low-energy SO levels of the neutral molecule to the ground state of the singly charged cation are identified by combining the MATI spectroscopic measurements with the MCQDPT2 calculations. The precise ionization energy is used to reassess the ionization energies and the reaction enthalpies of the Pr+ O → PrO+ + e- chemi-ionization reaction reported in the literature. An empirical formula that uses atomic electronic parameters is proposed to predict the ionization energies of lanthanide monoxides, and the empirical calculations match well with available precise experimental measurements.

Dispersion Interactions in Exciton-Localized States. Theory and Applications to π-π* and n-π* Excited States.

We address the problem of intermolecular interaction energy calculations in molecular complexes with localized excitons. Our focus is on the correct representation of the dispersion energy. We derive an extended Casimir-Polder formula for direct computation of this contribution through second order in the intermolecular interaction operator V̂. An alternative formula, accurate to infinite order in V̂, is derived within the framework of the adiabatic connection (AC) theory. We also propose a new parametrization of the VV10 nonlocal correlation density functional, so that it corrects the CASSCF energy for the dispersion contribution and can be applied to excited-state complexes. A numerical investigation is carried out for benzene, pyridine, and peptide complexes with the local exciton corresponding to the lowest π–π* or n– π* states. The extended Casimir-Polder formula is implemented in the framework of multiconfigurational symmetry-adapted perturbation theory, SAPT(MC). A SAPT(MC) analysis shows that the creation of a localized exciton affects mostly the electrostatic component of the interaction energy of investigated complexes. Nevertheless, the changes in Pauli repulsion and dispersion energies cannot be neglected. We verify the performance of several perturbation- and AC-based methods. Best results are obtained with a range-separated variant of an approximate AC approach employing extended random phase approximation and CASSCF wave functions.

Excited states of lutetium oxide and its singly charged cation.

Vibronic spectra of lutetium oxide (LuO) seeded in supersonic molecule beams are investigated with mass-analyzed threshold ionization (MATI) spectroscopy and second-order multiconfigurational quasi-degenerate perturbation (MCQDPT2) theory. Six states of LuO and four states of LuO+ are located by the MCQDPT2 calculations, and an a3Π(LuO+) ← C2Σ+ (LuΟ) transition is observed by the MATI measurement. The vibronic spectra show abnormal vibrational intervals for both the neural and cation excited states, and the abnormality is attributed to vibrational perturbations induced by interactions with neighboring states.

Protonation States of Molecular Groups in the Chromophore-Binding Site Modulate Properties of the Reversibly Switchable Fluorescent Protein rsEGFP2.

The role of protonation states of the chromophore and its neighboring amino acid side chains of the reversibly switching fluorescent protein rsEGFP2 upon photoswitching is characterized by molecular modeling methods. Numerous conformations of the chromophore-binding site in computationally derived model systems are obtained using the quantum chemistry and QM/MM approaches. Excitation energies are computed using the extended multiconfigurational quasidegenerate perturbation theory (XMCQDPT2). The obtained structures and absorption spectra allow us to provide an interpretation of the observed structural and spectral properties of rsEGFP2 in the active ON and inactive OFF states. The results demonstrate that in addition to the dominating anionic and neutral forms of the chromophore, the cationic and zwitterionic forms may participate in the photoswitching of rsEGFP2. Conformations and protonation forms of the Glu223 and His149 side chains in the chromophore-binding site play an essential role in stabilizing specific protonation forms of the chromophore.

Symmetry-Adapted Perturbation Theory Based on Multiconfigurational Wave Function Description of Monomers.

We present a formulation of the multiconfigurational (MC) wave function symmetry-adapted perturbation theory (SAPT). The method is applicable to noncovalent interactions between monomers which require a multiconfigurational description, in particular when the interacting system is strongly correlated or in an electronically excited state. SAPT(MC) is based on one- and two-particle reduced density matrices of the monomers and assumes the single-exchange approximation for the exchange energy contributions. Second-order terms are expressed through response properties from extended random phase approximation (ERPA). The dispersion components of SAPT(MC) have been introduced in our previous works [HapkaM.J. Chem. Theory Comput.2019, 15, 1016−102730525591; HapkaM.J. Chem. Theory Comput.2019, 15, 6712–672331670950]. SAPT(MC) is applied either with generalized valence bond perfect pairing (GVB) or with complete active space self-consistent field (CASSCF) treatment of the monomers. We discuss two model multireference systems: the H2 ··· H2 dimer in out-of-equilibrium geometries and interaction between the argon atom and excited state of ethylene. Using the C2H4* ··· Ar complex as an example, we examine second-order terms arising from negative transitions in the linear response function of an excited monomer. We demonstrate that the negative-transition terms must be accounted for to ensure qualitative prediction of induction and dispersion energies and develop a procedure allowing for their computation. Factors limiting the accuracy of SAPT(MC) are discussed in comparison with other second-order SAPT schemes on a data set of small single-reference dimers.

Improving half-projected spin-contaminated wave functions by multi-configuration perturbation theory.

Allowing triplet components of individual geminals, spin-contaminated strongly orthogonal geminal wave functions may emerge, which can be ameliorated by spin-projection techniques. Of the latter, half-projection was previously shown to be useful, offering a compromise between the amount of remaining spin-contamination and the violation of size consistency generated by projection. This paper investigates how a half-projected spin-contaminated geminal wave function can be improved by multi-configuration perturbation theory to incorporate dynamical correlation effects.

A SA-CASSCF and MS-CASPT2 study on the electronic structure of nitrosobenzene and its relation to its dissociation dynamics.

The photodissociation channels of nitrosobenzene (PhNO) induced by a 255 nm photolytic wavelength have been studied using the complete active space self-consistent method and the multistate second-order multiconfigurational perturbation theory. It is found that there exists a triplet route for photodissociation of the molecule. The reaction mechanism consists of a complex cascade of nonadiabatic electronic transitions involving triple and double conical intersections as well as intersystem crossing. Several of the relevant states (S2, S4, and S5 states) correspond to double excitations. It is worth noting that the last step of the photodissociation implies an internal conversion process. The experimentally observed velocity pattern of the NO fragment is a signature of such a conical intersection.