Multiconfigurational Quasidegenerate Perturbation Theory Research Articles

Structure and Properties of Precursor/Successor Complex and Transition State of the FeCl2+/Fe2+ Electron Self-Exchange Reaction via the Inner-Sphere Pathway

The electron self-exchange reaction FeCl(OH2)5(2+) + Fe(OH2)6(2+) → Fe(OH2)6(2+) + FeCl(OH2)5(2+), proceeding via the inner-sphere pathway, was investigated with quantum chemical methods. Geometry and vibrational frequencies of the precursor/successor complex, (H2O)5Fe(III)ClFe(II)(OH2)5(4+)/(H2O)5Fe(II)ClFe(III)(OH2)5(4+) (P/S), and the transition state, (H2O)5FeClFe(OH2)5(4+⧧) (TS), were computed with the LC-BOP functional and CPCM hydration. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (Hab) and the electronic energies were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory (XGMC-QDPT2) and spin-orbit configuration interaction (SO-CI). Since the Fe···Fe distance changes considerably along the electron transfer step, the transformation P → TS → S, equations based on the hypothesis of a fixed donor-acceptor distance cannot be applied. Hence, the rate constant for the electron transfer step (ket) was calculated as described previously (Rotzinger, F. P. Inorg. Chem. 2014, 53, 9923). ket is very fast, ∼9.4 × 10(8)-6.6 × 10(9) s(-1) at 0 °C. The experimental rate constant of the title reaction (k) is much slower and controlled by the formation of the precursor complex. The substitution of a water ligand by FeCl(OH2)5(2+) at Fe(OH2)6(2+) is rate-determining.

Investigation of the water exchange mechanism of the Plutonyl(VI) and Uranyl(VI) ions with quantum chemical methods

The water exchange reactions of [PuO2(OH2)5]2+ and [UO2(OH2)5]2+ were investigated with density functional theory (DFT) and wave function theory (WFT). Geometries and vibrational frequencies were calculated with DFT and CPCM hydration. The electronic energies were evaluated with general multiconfiguration quasi-degenerate second-order perturbation theory (GMC-QDPT2). Spin-orbit (SO) effects, computed with SO configuration interaction (SO–CI), are negligible. Both Actinyl(VI) ions react via an associative exchange mechanism, most likely Ia. The Gibbs activation energies (ΔG‡) at 25 °C are 33–34 and 30–37 kJ mol−1 for [PuO2(OH2)5]2+ and [UO2(OH2)5]2+, respectively. ΔG‡ for dissociative mechanisms (D, Id) is higher by more than 15 kJ mol−1.

Model space diabatization for quantum photochemistry.

Diabatization is a procedure that transforms multiple adiabatic electronic states to a new representation in which the potential energy surfaces and the couplings between states due to the electronic Hamiltonian operator are smooth, and the couplings due to nuclear momentum are negligible. In this work, we propose a simple and general diabatization strategy, called model space diabatization, that is applicable to multi-configuration quasidegenerate perturbation theory (MC-QDPT) or its extended version (XMC-QDPT). An advantage over previous diabatization schemes is that dynamical correlation calculations are based on standard post-multi-configurational self-consistent field (MCSCF) multi-state methods even though the diabatization is based on state-averaged MCSCF results. The strategy is illustrated here by applications to LiH, LiF, and thioanisole, with the fourfold-way diabatization and XMC-QDPT, and the results illustrate its validity.

Triplet–singlet gap in structurally flexible organic diradicals

A key factor in the search of high-spin ground state purely organic molecules concerns the effect of the inherent non-rigid structures on the magnetic and optical properties. This structural feature has not been properly addressed in previous theoretical works. Here, based on the experimentally characterized high-spin ground state of dendritic and star-branched polyradicals, we study four alternant hydrocarbon biradicals that intend to model these effects and, at the same time, provide a first step toward understanding more extended experimental structures. A series of density functional theory (DFT) and of wave function-based methods have been used to explore the richness of structural minima in the corresponding potential energy surfaces and to discuss its effect on the triplet–singlet gap of the proposed model systems. For a given model, the DFT-based B3LYP, M06-2X and MN-12SX methods provide a consistent description. Likewise, a multiconfigurational quasi-degenerate perturbation theory approach with the minimal π space as CASSCF reference is found to provide unbiased results. Despite the conformational richness found for these systems, they all can be described by a reduced set of values referred to only two structural parameters, being those the dihedral angles between the phenyl rings. For a given model, there is no significant change in the triplet–singlet gap depending on the chosen local minima.

Structure and properties of the precursor/successor complex and transition state of the CrCl²⁺/Cr²⁺ electron self-exchange reaction via the inner-sphere pathway.

The electron self-exchange reaction CrCl(OH2)5(2+) + Cr(OH2)6(2+) → Cr(OH2)6(2+) + CrCl(OH2)5(2+), proceeding via the inner-sphere pathway, was investigated with quantum-chemical methods. Geometry and vibrational frequencies of the precursor/successor (P/S) complex, (H2O)5Cr(III)ClCr(II)(OH2)5(4+)/(H2O)5Cr(II)ClCr(III)(OH2)5(4+), and the transition state (TS), (H2O)5CrClCr(OH2)5(4+‡), were computed with density functional theory (DFT) and conductor polarizable continuum model hydration. Consistent data were obtained solely with long-range-corrected functionals, whereby in this study, LC-BOP was used. Bent and linear structures were computed for the TS and P/S. The electronic coupling matrix element (H(ab)) and the reorganizational energy (λ) were calculated with multistate extended general multiconfiguration quasi-degenerate second-order perturbation theory. The nuclear tunneling factor (Γ(n)), the nuclear frequency factor (ν(n)), the electronic frequency factor (ν(el)), the electron transmission coefficient (κ(el)), and the first-order rate constant (k(et)) for the electron-transfer step (the conversion of the precursor complex into the successor complex) were calculated based on the imaginary frequency (ν(‡)) of the TS, the Gibbs activation energy (ΔG(‡)), H(ab), and λ. The formation of the precursor complex via water substitution at Cr(OH2)6(2+) was also investigated with DFT and found to be very fast. Thus, the electron-transfer step is rate-determining. For the substitution reaction, only a bent TS structure could be obtained. The overall rate constant (k) was estimated as the product K(A)k(et), whereby K(A) is the equilibrium constant for the formation of the ion aggregate of the reactants Cr(OH2)6(2+) and CrCl(OH2)5(2+), Cr(H2O)6·CrCl(OH2)5(4+) (IAR). k calculated for the bent and linear isomers agrees with the experimental value.

The reliability of DFT methods to predict electronic structures and minimum energy crossing point for [FeIVO](OH)2 models: A comparison study with MCQDPT method

In order to test the reliability of DFT methods for calculating electronic structures of [Fe(IV)O] system, detailed calculations of [Fe(IV)O](OH)2 models were performed for several low-energy states using multiconfiguration quasidegenerate perturbation theory (MCQDPT) as well as DFT-based methods. The minimum energy crossing points (MECP) of (5)A1/(5)B2 and (3)B2/(5)B2 were investigated based on Lagrange-Newton approach. The results show that M06 functional produce energy gaps close to those of MCQDPT results. Another topic in this article is that the electron configurations of [Fe(IV)O](OH)2 models strongly depend on the type of surface ligand used, and the two lowest states of these can facile transition each other by the MECP. The practicability of M06 method in locating the MECP is validated by the results of MCQDPT which demonstrate the two-state reactivity (TSR) can be studied with proper DFT method. These inspections provide the basis for further TSR study of larger [Fe(IV)O] system.

The characteristics of excited states for HF+ ion under spin-orbit coupling

The characteristics of ground state X2Πi and the first excited state A2Σ+ of HF+ under spin-orbit coupling are studied by using the multi-configuration quasi-degenerate perturbation theory. The vertical excited energy is v[2Π1/2 (v = 0)→ X2Π3/2(v = 0)] = 285.176 cm-1, and the potential energy curves of the splitting electronic states X2Π3/2, 2Π1/2 of X2Πi are obtained. The analytical potential functions of these states are derived by employing the Murrell- Sorbie function (M-S) and the least-square fitting method, and then the spectroscopic constants for X2Π3/2, 2Π1/2 and A2Σ+ are derived from the M-S function. All the spectroscopic data and the analytical potential functions for states X2Π3/2 and 2Π1/2 are given for the first time in our calculation.

Diabatic Molecular Orbitals, Potential Energies, and Potential Energy Surface Couplings by the 4-fold Way for Photodissociation of Phenol.

Complete-active-space self-consistent-field (CASSCF) calculations provide useful reference wave functions for configuration interaction or perturbation theory calculations of excited-state potential energy surfaces including dynamical electron correlation. However, the canonical molecular orbitals (MOs) of CASSCF calculations usually have mixed character in regions of strong interaction of two or more electronic states; therefore, they are unsuitable for diabatization using the configurational uniformity approach. Here, CASSCF diabatic MOs for phenol have been obtained by the 4-fold way, and comparison to the CASSCF canonical MOs shows that they are much smoother. Using these smooth CASSCF diabatic MOs, we performed direct diabatization calculations for the three low-lying states ((1)ππ, (1)ππ*, and (1)πσ*) and their diabatic (scalar) couplings at the dynamically correlated multiconfiguration quasidegenerate perturbation theory (MC-QDPT) level. We present calculations along the O-H stretching and C-C-O-H torsion coordinates for the nonadiabatic photodissociation of phenol to the phenoxyl radical and hydrogen atom. The seams of (1)ππ*/(1)πσ* and (1)ππ/(1)πσ* diabatic crossings are plotted as functions of these coordinates. We also present diabatization calculations for displacements along the out-of-plane ring distortion modes 16a and 16b of the phenyl group. The dominant coupling modes of the two conical intersections ((1)ππ*/(1)πσ* and (1)ππ/(1)πσ*) are discussed. The present diabatization method is confirmed to be valid even for significantly distorted ring structures by diabatization calculations along a reaction path connecting the planar equilibrium geometry of phenol to its strongly distorted prefulvenic form. The present work provides insight into the mode specificity of phenol photodissociation and shows that diabatization at the MC-QDPT level employing CASSCF diabatic MOs can be a good starting point for multidimensional dynamics calculations of photochemical reactions.

Direct diabatization of electronic states by the fourfold-way: Including dynamical correlation by multi-configuration quasidegenerate perturbation theory with complete active space self-consistent-field diabatic molecular orbitals

We propose a new scheme for the direct diabatization of MC-QDPT wave functions. Our new scheme utilizes CASSCF diabatic molecular orbitals (DMOs); this is conceptually simpler than the previous approach and can lead to smoother diabatic potentials. We validated the new diabatization scheme, in comparison to CASSCF diabatization and to the original MC-QDPT diabatization scheme, for two test cases, the dissociation of LiF and the reaction of Li+FH→LiF+H. The results with our new scheme suggest that the new scheme with CASSCF DMOs would be a good choice for nonadiabatic dynamics studies in the future.

Quantum chemical modeling of components of dye-sensitized solar cells

Ab initio approaches of quantum chemistry, including the fragment molecular orbital (FMO) method, as well as the multiconfigurational quasidegenerate perturbation theory (XMCQDPT2) and time-dependent density functional theory (TD DFT) were applied to compute optical spectra of a polyene dye molecule on the surface of titanium dioxide.

Electronic structure of the S1 state in methylcobalamin: Insight from CASSCF/MC‐XQDPT2, EOM‐CCSD, and TD‐DFT calculations

The methylcobalamin cofactor (MeCbl), which is one of the biologically active forms of vitamin B12, has been the subject of many spectroscopic and theoretical investigations. Traditionally, the lowest-energy part of the photoabsorption spectrum of MeCbl (the so-called α/β band) has been interpreted as an S0→S1 electronic transition dominated by π→π* excitations associated with the C=C stretching of the corrin ring. However, a more quantitative band-shape analysis of the α/β spectral region, along with circular dichroism (CD), magnetic CD, and resonance Raman data, has revealed the presence of a second electronic transition that involves the Co-C(Me) bond weakening. Conversely, the lowest-energy excitations based on transient absorption spectroscopy measurements have been interpreted as metal-to-ligand charge transfer (MLCT) transitions. To resolve the existing controversy about the interpretation of the S1 state of MeCbl, calculations have been performed using two independent ab initio wavefunction-based methods. These include the modified variant of the second-order multiconfigurational quasi-degenerate perturbation theory (MC-XQDPT2), using complete active space self-consistent field orbitals, and the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) approach using restricted Hartree-Fock orbitals. It is shown that both ab initio methods provide a consistent description of the S1 state as having an MLCT character. In addition, the performance of different types of functionals, including hybrid (B3LYP, MPW1PW91, TPSSh), generalized-gradient-approximation-type (GGA-type) (BP86, BLYP, MPWPW91), meta-GGA (TPSS), and range-separated (CAM-B3LYP, LC-BLYP) approaches, has been examined and the results of the corresponding time-dependent density functional theory calculations have been benchmarked against the MC-XQDPT2 and EOM-CCSD data. The hybrid functionals support the interpretation in which the S1 state represents a π→π* transition localized on corrin, while pure GGA, meta-GGA, and LC-BLYP functionals produce results consistent with the MLCT assignment.

Pyrazine excited states revisited using the extended multi-state complete active space second-order perturbation method

We demonstrate that the recently developed extended multi-state complete active space second-order perturbation theory (XMS-CASPT2) [Shiozaki et al., J. Chem. Phys., 2011, 135, 081106] provides qualitatively correct potential energy surfaces for low-lying excited singlet states of pyrazine, while the potential energy surfaces of the standard MS-CASPT2 methods are ill-behaved near the crossing point of two reference potential energy surfaces. The XMS-CASPT2 method is based on the extended multi-configuration quasi-degenerate perturbation theory proposed earlier by Granovsky [J. Chem. Phys., 2011, 134, 214113]. We show that the conical intersection at the XMS-CASPT2 level can be described without artifacts if the entire method is invariant with respect to any unitary rotations of the reference functions. The photoabsorption spectra of the 1(1)B(3u) and 1(1)B(2u) states of pyrazine are simulated, based on a vibronic-coupling model Hamiltonian. The XMS-CASPT2 spectrum of the 1(1)B(3u) band is found to be comparable to the one computed by a more expensive multireference configuration interaction (MRCI) method, while the XMS-CASPT2 simulation of the 1(1)B(2u) band is slightly inferior to the MRCI one.

Photochemistry in a dense manifold of electronic states: Photodissociation of CH2ClBr

We report electronically nonadiabatic dynamics calculations including spin-orbit coupling for the photodissociation of CH(2)ClBr to yield Cl((2)P(3∕2)), Cl((2)P(1∕2)), Br((2)P(3∕2)), and Br((2)P(1∕2)). The potential energy is a 24 × 24 matrix (divided up here into four 6 × 6 blocks in a first approximation to the problem), in a spin-coupled fully diabatic representation obtained by combining the spin-free fourfold way with single-center spin-orbit coupling constants. The spin-free calculations are carried out by multiconfiguration quasidegenerate perturbation theory, and the fully diabatic potentials including spin-orbit coupling are fit to a matrix reactive force field. The dynamics are carried out by the coherent switches with decay of mixing method in the diabatic representation. The results show qualitative agreement with experiment.

Natural Spinors Reveal How the Spin–Orbit Coupling Affects the Jahn–Teller Distortions in the Hexafluorotungstate(V) Anion

We investigate the Jahn-Teller distortions in the hexafluorotungstate(V) anion (WF6(-)) by applying the recently developed concept of natural spinors (spin-orbitals) and show that they are a very powerful tool providing simple and clear pictorial explanation for the spin-orbit effect in determining the structure of the anion. The calculations are performed at the levels of spin-orbit configuration interaction and multiconfigurational quasi-degenerate perturbation theory. The hexafluorotungstate(V) anion represents a very rare example of spin-orbit coupling enhancing the Jahn-Teller distortion, and the natural spinor analysis gives a clear interpretation of this enhancement. Advantages of using the natural spinors are explored and explained in detail in this case study.

Toward Molecular-Level Characterization of Photoinduced Decarboxylation of the Green Fluorescent Protein: Accessibility of the Charge-Transfer States.

Irradiation of the green fluorescent protein (GFP) by intense violet or UV light leads to decarboxylation of the Glu222 side chain in the vicinity of the chromophore (Chro). This phenomenon is utilized in optical highlighters, such as photoactivatable GFP (PA-GFP). Using state-of-the-art quantum chemical calculations, we investigate the feasibility of the mechanism proposed in the experimental studies [van Thor et al. Nature Struct. Biol.2002, 9, 37-41; Bell et al. J. Am. Chem. Soc.2003, 125, 37-41]. It was hypothesized that a primary event of this photoconversion involves population of a charge-transfer (CT) state via either the first excited state S1 when using longer wavelength (404 and 476 nm) or a higher excited state when using higher energy radiation (254 and 280 nm). Based on the results of electronic structure calculations, we identify these critical CT states (produced by electron transfer from Glu to electronically excited Chro) and show that they are accessible via different routes, i.e., either directly, by one-photon absorption, or through a two-step excitation via S1. The calculations are performed for model systems representing the chromophore and the key nearby residues using two complementary approaches: (i) the multiconfigurational quasidegenerate perturbation theory of second order with the occupation restricted multiple active space scheme for configuration selection in the multiconfigurational self-consistent field reference; and (ii) the single-reference configuration interaction singles method with perturbative doubles that does not involve active space selection. We examined electronic transitions with nonzero oscillator strengths in the UV and visible range between the electronic states involving the Chro and Glu residues. Both methods predict the existence of CT states with nonzero oscillator strength in the UV range and a local excited state of the chromophore accessible via S1 that may lead to the target CT state. The results suggest several possible scenarios for the primary photoconversion event. We also demonstrate that the point mutation Thr203His exploited in PA-GFP results in shifting the light wavelength to access the CT up to 20 nm, which suggests a possibility of a rational design of photoactivatable proteins in silico.

Low-lying electronic excitations and optical absorption spectra of the black dye sensitizer: a first-principles study

We report on ab-initio calculations of the electronic structure and optical absorption response of the black dye sensitizer in gas phase. We show that, despite the large size of this molecule, the second-order multiconfiguration quasi-degenerate perturbation theory (MC-QDPT) can be used to calculate vertical excitation energies, oscillator strengths and optical absorption spectra. The zeroth-order reference states entering perturbation calculations are complete active space (CAS) configuration interaction (CI) wave functions computed for 12 active electrons distributed in 12 active orbitals. We found that the CI approach is not enough for taking into account the strong dynamical correlation effects in this system. In fact, the excitation energies of the CAS-CI target states are strongly renormalized by the MC-QDPT calculations. In the calculated absorption spectra, the analysis of the perturbed wavefunctions revealed that the stronger absorption bands correspond to metal-to-ligand and ligand-to-ligand charge transfer processes. Comparison with independent time-dependent extension (TDDFT) calculations performed with different functionals shows that corrections to the long-range behavior of the functional is pivotal to achieve agreement with the MC-QDPT results.

Spin-orbit effects in the ground X2Π state and two low-lying excited valence states B2Π and L′2Φ for NO

The potential energy curves and spectroscopic constants B e , ω e , ω e χ e , α e , D e of the six Ω states (X 2Π1/2, 3/2, B 2Π1/2, 3/2 and L ′2Φ5/2, 7/2) of the NO radical molecule were calculated using spin-orbit multi-configuration quasi-degenerate perturbation theory (SO-MCQDPT). The spin-orbit coupling effect was considered via the state interaction approach with the full Breit-Pauli Hamiltonian. The spin-orbit splitting energy between the X 2Π1/2 and X 2Π3/2 states of the NO radical is 129.61 cm-1, which agrees reasonably well with the experimental value of 123.13 cm-1. For the B 2Π1/2, 3/2 states, the spin-orbit coupling (SOC) splitting energy is 35.99 cm-1, the corresponding experimental value is 31.7 cm-1. The SOC splitting value of the L ′2Φ5/2, 7/2 states was calculated to be 103.2 cm-1. The spectroscopic constants R e , ω e , ω e χ e , B e , α e , D e are in reasonable agreement with available experimental and theoretical data for the six Ω states.

Ab Initio Studies of Aromatic Excimers Using Multiconfiguration Quasi-Degenerate Perturbation Theory

The aromatic excimers of benzene, naphthalene, anthracene, pyrene, and perylene are systematically investigated using the multiconfiguration quasi-degenerate perturbation theory (MCQDPT) method, which is one of high-level ab initio quantum chemical methods. The reference configuration space for MCQDPT is carefully designed for an appropriate description of the target electronic state with a tractable computational cost. The dimers with eclipsed parallel arrangement are investigated. The basis set dependence of the selected spectroscopic parameters is examined for the benzene and naphthalene dimers, and that of the excimer binding energy is found to be significant. In contrast, the equilibrium intermolecular distance and excimer fluorescence energy are less sensitive to the size of the basis sets used, and they agree with the corresponding experimental values, even with a nonextensive basis set size. The calculated spectroscopic parameters for anthracene, pyrene, and perylene dimers are also in good agreement with the experimental results. The electronic properties of the excimers are discussed in relation to those of the corresponding monomers. The wave functions of the excimers are analyzed in detail to clarify the origin of the attractive nature between the two monomers.

Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory

The distinctive desirable features, both mathematically and physically meaningful, for all partially contracted multi-state multi-reference perturbation theories (MS-MR-PT) are explicitly formulated. The original approach to MS-MR-PT theory, called extended multi-configuration quasi-degenerate perturbation theory (XMCQDPT), having most, if not all, of the desirable properties is introduced. The new method is applied at the second order of perturbation theory (XMCQDPT2) to the 1(1)A(')-2(1)A(') conical intersection in allene molecule, the avoided crossing in LiF molecule, and the 1(1)A(1) to 2(1)A(1) electronic transition in cis-1,3-butadiene. The new theory has several advantages compared to those of well-established approaches, such as second order multi-configuration quasi-degenerate perturbation theory and multi-state-second order complete active space perturbation theory. The analysis of the prevalent approaches to the MS-MR-PT theory performed within the framework of the XMCQDPT theory unveils the origin of their common inherent problems. We describe the efficient implementation strategy that makes XMCQDPT2 an especially useful general-purpose tool in the high-level modeling of small to large molecular systems.

Solvent-Induced Shifts in Electronic Spectra of Uracil

Highly accurate excitation spectra are predicted for the low-lying n-π* and π-π* states of uracil for both the gas phase and in water employing the complete active space self-consistent field (CASSCF) and multiconfigurational quasidegenerate perturbation theory (MCQDPT) methods. Implementation of the effective fragment potential (EFP) solvent method with CASSCF and MCQDPT enables the prediction of highly accurate solvated spectra, along with a direct interpretation of solvent shifts in terms of intermolecular interactions between solvent and solute. Solvent shifts of the n-π* and π-π* excited states arise mainly from a change in the electrostatic interaction between solvent and solute upon photoexcitation. Polarization (induction) interactions contribute about 0.1 eV to the solvent-shifted excitation. The blue shift of the n-π* state is found to be 0.43 eV and the red shift of the π-π* state is found to be -0.26 eV. Furthermore, the spectra show that in solution the π-π* state is 0.4 eV lower in energy than the n-π* state.