Quasi-degenerate Perturbation Theory Research Articles

Electronic Excited States and UV-Vis Absorption Spectra of the Dihydropyrene/Cyclophanediene Photochromic Couple: a Theoretical Investigation.

Dihydropyrene (DHP)/cyclophanediene (CPD) is a fascinating photoswitchable organic system displaying negative photochromism. Upon irradiation in the visible region, the colored DHP can be converted to its open-ring CPD colorless isomer, which can be converted back to DHP by UV light. DHP and CPD thus possess very different absorption spectra whose absorption bands have never been assigned in detail so far. In this work, we characterize the vertical electronic transitions of the first six and seven excited states of DHP and CPD, respectively, aiming for a realistic comparison with experiment. We used state-of-the-art electronic structure methods [e.g., complete active space second-order perturbation theory (CASPT2), n-electron valence-state perturbation theory (NEVPT2), extended multiconfigurational quasi-degenerate perturbation theory (XMCQDPT2), and third-order algebraic diagrammatic construction ADC(3)] capable of describing differential electron correlation. Vertical transition energies were also computed with time-dependent density functional theory (TD-DFT) and compared to these accurate methods. After the reliability of TD-DFT was validated for the main optical transitions, this efficient method was used to simulate the absorption spectra of DHP and CPD in the framework of the Franck-Condon Herzberg-Teller approximation and also using the nuclear ensemble approach. Overall, for both methods, the simulated absorption spectra reproduce nicely the main spectral features of the DHP and CPD isomers, that is, the main four absorption bands of increasing intensity of DHP and the absorption rise below 300 nm for CPD.

The combination of multipartitioning of the Hamiltonian with canonical Van Vleck perturbation theory leads to a Hermitian variant of quasidegenerate N-electron valence perturbation theory.

Many recent developments in the area of multistate multireference perturbation theories focused on methods that use a state-averaged 0th order Hamiltonian. We recently found that the dynamic correlation dressed complete active space method fails in describing ligand field and charge transfer states in a balanced way precisely because it uses a state-averaged 0th order Hamiltonian [L. Lang and F. Neese, J. Chem. Phys. 150, 104104 (2019)]. The multipartitioning idea allows the use of state-specific 0th order Hamiltonians in a multistate framework and could therefore alleviate the mentioned problem. However, the effective Hamiltonian is non-Hermitian in the traditional formulation of multipartitioning, which can lead to unphysical behavior, especially for nearly degenerate states. In order to achieve a more balanced treatment of states with different physical character and at the same time have a Hermitian effective Hamiltonian, we combine in this work multipartitioning with canonical Van Vleck perturbation theory. At the 2nd order, the result is a Hermitian variant of multipartitioning quasidegenerate N-electron valence state perturbation theory. The effect of model space noninvariance of the method is discussed and the benefit of a Hermitian formulation is highlighted with numerical examples. The method is shown to give good results for the calculation of electronic transitions of the [CuCl4]2 -complex and for the calculation of electron paramagnetic resonance parameters, which are two examples where the balance between ligand field and charge transfer configurations is of utmost importance.

Ab initio study on the excited states of pyrene and its derivatives using multi-reference perturbation theory methods.

Low-lying singlet excited states of pyrene derivatives originated from the 1La and 1Lb states of pyrene have decisive influences on their absorption and fluorescence emission behaviors. Calculation of these excited states with quantitative accuracy is required for the theoretical design of pyrene derivatives tailored to target applications; this has been a long-standing challenge for ab initio quantum chemical calculations. In this study, we explore an adequate computational scheme through calculations of pyrene and its phenyl-substituted derivatives using multi-reference perturbation theory (MRPT) methods. All valence π orbitals on the pyrene moiety were assigned to the active orbitals. Computational load was reduced by restricting the electron excitations within the active orbitals in the preparation of reference configuration space. A generalized multi-configuration quasi-degenerate perturbation theory (GMCQDPT) was adopted to treat the reference space other than the complete active space. The calculated 1La and 1Lb excitation energies of pyrene are in good agreement with the experimental values. Calculations of 1,3,6,8-tetraphenyl pyrene suggest that the energetic ordering of 1La and 1Lb is inverted through tetraphenyl substitution and its lowest singlet excited state is the 1La parentage of pyrene, which is consistent with the experimentally deduced scheme. These results are not readily obtained by MRPT calculations with a limited number of active orbitals and single-reference theory calculations. Diphenyl pyrenes (DPPy) were also calculated at the same level of theory to investigate the dependence on the substitution positions of phenyl groups.

Analytical Gradient Theory for Quasidegenerate N-Electron Valence State Perturbation Theory (QD-NEVPT2).

Analytical nuclear gradient and derivative coupling theories for the quasidegenerate N-electron valence state perturbation theory using state-averaged orbitals and density matrices are formulated and implemented. In our implementation, the Lagrangian formalism is employed to derive the working expressions. By implementing a direct algorithm for the four-particle reduced density matrix derivatives, large active spaces up to (12e,12o) are routinely tractable. The applicability of the current algorithm is tested for optimizing the minimal energy conical intersections of the representative photochemical systems: ethylene, a retinal protonated Schiff base (penta-2,4-dieniminium cation, PSB3) model, and a green fluorescent protein chromophore (para-hydroxybenzilideneimidazolin-5-one, pHBI) model. For ethylene, we show that the optimized geometries reasonably agree with the previous geometries using the (extended) multistate second-order complete active space perturbation theory and the multireference configuration interaction with the singles and doubles method. For PSB3, we investigate the effect of the basis set selections, ranging from cc-pVDZ to cc-pV5Z, and the effect of noninvariance in describing conical intersections. For pHBI, we test two active spaces, (4e,3o) and (12e,11o), and survey the active-space dependence. We also discuss the computational cost, the parallel efficiency, and the future applicability of the current algorithm.

NaI revisited: Theoretical investigation of predissociation via ultrafast XUV transient absorption spectroscopy.

Avoided crossings can trigger abrupt changes of electronic character and redirect the outcomes of photochemical reactions. Here, we report a theoretical investigation into core-level spectroscopic probing of predissociation dynamics of sodium iodide (NaI), a prototype system for studies of avoided-crossing dynamics. The elegant femtochemistry work of Zewail and co-workers pioneered the real-time dynamics of NaI, detecting the Na atoms bursting forth from the avoided crossing and the residual NaI molecules oscillating inside the quasibound potential. The simulated results show that core-level spectroscopy not only observes these integrated outcomes but also provides a direct measure of the abrupt switching of electronic character at the avoided crossing. The valence and core-excited electronic structures of NaI are computed by spin-orbit general multiconfigurational quasidegenerate perturbation theory, from which core-level absorption spectra of the predissociation dynamics are constructed. The wave-packet motion on the covalent potential is continuously mapped as shifts in the absorption energies, and the switching between the covalent and ionic character at the avoided crossing is characterized as the sharp rise and fall of the Na+ signal. The Na+ signal is found to be insensitive to the wave-packet motion in the asymptotic part of the ionic potential, which, in turn, enables a direct measure of the nonadiabatic crossing probability excluding the effect of wave-packet broadening.

Full-dimensional three-state potential energy surfaces and state couplings for photodissociation of thiophenol.

An analytic full-dimensional diabatic potential energy matrix (DPEM) for the lowest three singlet states of thiophenol (C6H5SH) at geometries accessible during photodissociation is constructed using the anchor points reactive potential (APRP) scheme. The data set used for modeling is obtained from electronic structure calculations including dynamic correlation via excitations into the virtual space of a three-state multiconfiguration self-consistent field calculation. The resulting DPEM is a function of all the internal coordinates of thiophenol. The DPEM as a function of the S-H bond stretch and C-C-S-H torsion and the diabatic couplings along two in-plane bend modes and nine out-of-plane distortion modes are computed using extended multiconfigurational quasidegenerate perturbation theory followed by the fourfold way determination of diabatic molecular orbitals and model space diabatization by configurational uniformity, and this dependence of the DPEM is represented by general functional forms. Potentials along 31 tertiary internal degrees of freedom are modeled with system-dependent, primary-coordinate-dependent nonreactive molecular mechanics-type force fields that are parameterized by Cartesian Hessians calculated by generalized Kohn-Sham density functional theory. Adiabatic potential energy surfaces (PESs) and nonadiabatic couplings are obtained by a transformation of the DPEM. The topography of the APRP PESs is characterized by vertical excitation energies, equilibrium geometries, vibrational frequencies, and conical intersections, and we find good agreement with available reference data. This analytic DPEM is suitable for full-dimensional electronically nonadiabatic molecular dynamics calculations of the photodissociation of thiophenol with analytic gradients in either the adiabatic or diabatic representation.

Multistate Multiconfiguration Quantum Chemical Computation of the Two-Photon Absorption Spectra of Bovine Rhodopsin.

Recently, progress in IR sources has led to the discovery that humans can detect infrared (IR) light. This is hypothesized to be due to the two-photon absorption (TPA) events promoting the retina dim-light rod photoreceptor rhodopsin to the same excited state populated via one-photon absorption (OPA). Here, we combine quantum mechanics/molecular mechanics and extended multiconfiguration quasi-degenerate perturbation theory calculations to simulate the TPA spectrum of bovine rhodopsin (Rh) as a model for the human photoreceptor. The results show that the TPA spectrum of Rh has an intense S0 → S1 band but shows also S0 → S2 and S0 → S3 transitions whose intensities, relative to the S0 → S1 band, are significantly increased when compared to the corresponding bands of the OPA spectrum. In conclusion, we show that IR light in the 950 nm region can be perceived by rod photoreceptors, thus supporting the two-photon origin of the IR perception. We also found that the same photoreceptor can perceive red (i.e., close to 680 nm) light provided that TPA induces population of S2.

Direct diabatization and analytic representation of coupled potential energy surfaces and couplings for the reactive quenching of the excited 2Σ+ state of OH by molecular hydrogen.

We have employed extended multiconfiguration quasidegenerate perturbation theory, fourfold-way diabatic molecular orbitals, and configurational uniformity to develop a global three-state diabatic representation of the potential energy surfaces and their couplings for the electronically nonadiabatic reaction OH* + H2 → H2O + H, where * denotes electronic excitation to the A 2Σ+ state. To achieve sign consistency of the computed diabatic couplings, we developed a graphics processing unit-accelerated algorithm called the cluster-growing algorithm. Having obtained consistent signs of the diabatic couplings, we fit the diabatic matrix elements (which consist of the diabatic potentials and the diabatic couplings) to analytic representations. Adiabatic potential energy surfaces are generated by diagonalizing the 3 × 3 diabatic potential energy matrix. The comparisons between the fitted and computed diabatic matrix elements and between the originally computed adiabatic potential energy surfaces and those generated from the fits indicate that the current fit is accurate enough for dynamical studies, and it may be used for quantal or semiclassical dynamics calculations.

In-plane magnetoelectric response in bilayer graphene

A graphene bilayer shows an unusual magnetoelectric response whose magnitude is controlled by the valley-isospin density, making it possible to link magnetoelectric behavior to valleytronics. Complementary to previous studies, we consider the effect of static homogeneous electric and magnetic fields that are oriented parallel to the bilayer's plane. Starting from a tight-binding description and using quasi-degenerate perturbation theory, the low-energy Hamiltonian is derived including all relevant magnetoelectric terms whose prefactors are expressed in terms of tight-binding parameters. We confirm the existence of an expected axion-type pseudoscalar term, which turns out to have the same sign and about twice the magnitude of the previously obtained out-of-plane counterpart. Additionally, small anisotropic corrections to the magnetoelectric tensor are found that are fundamentally related to the skew interlayer hopping parameter $\gamma_4$. We discuss possible ways to identify magnetoelectric effects by distinctive features in the optical conductivity.

Interaction of CH4 with Electronically Excited O2: Ab Initio Potential Energy Surfaces and Reaction Kinetics

Multireference quantum chemical research with the aid of complete active space self-consistent field approach was performed to study the elementary reactions of $${{\text {CH}}_4}$$ with $${\text {O}}_2$$ in $${a^1\varDelta _g}$$ , $${b^1\varSigma _g^+}$$ , $${c^1\varSigma _u^-}$$ , and $${A^{\prime 3} \varDelta _u}$$ electronically excited states highly relevant for plasma-assisted combustion and for plasma-chemical fuel reforming. The thermodynamically and kinetically favorable reaction pathways and likely intersystem crossings for the first step of the methane oxidation have been found out. The key energy values were refined based upon the extended multiconfiguration quasi-degenerate 2nd-order perturbation theory. It has been exhibited that the reaction of $${{\text {O}}_2(a^1\varDelta _g)}$$ and $${{\text {O}}_2(A^{\prime 3} \varDelta _u)}$$ with $${{\text {CH}}_4}$$ proceeds through the abstraction of hydrogen with fairly low energy barriers that led to the formation of the $$\hbox {HO}_2$$ molecule in $${^2A^{\prime \prime }}$$ and $${^2A^{\prime }}$$ electronic states, respectively. These results were compared with the findings of previous theoretical investigations. The oxygen molecule in singlet sigma b state was evinced to be nonreactive with regard to the methane. However, for $${c^1\varSigma _u^-}$$ state, the reactive interaction was nevertheless found possible due to the significant probability of the nonadiabatic transitions. Appropriate thermal rate constants for revealed channels have been calculated employing variational transition-state theory and capture approximation. Corresponding three-parameter Arrhenius expressions for the broad temperature range ( $$T=300$$ –3000 K) were reported.

Efficient Implementation of the Second-Order Quasidegenerate Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: Is It Possible To Use Hartree-Fock Orbitals for a Multiconfigurational Perturbation Theory?

The high cost of common multireference second-order perturbation theory (MRPT2) methods compared with the single-reference variant (MP2) arises from the expensive complete active space self-consistent field (CASSCF) orbital optimization step. Furthermore, the use of conventional four-index electron repulsion integrals (ERIs) prevents their application to larger molecular systems due to expensive I/O procedures. To address these bottlenecks of the multiconfigurational second-order quasidegenerate perturbation theory (MC-QDPT2), an efficient implementation of QDPT2 with the density-fitting (DF) and Cholesky decomposition (CD) approximations, denoted by DF-QDPT2 and CD-QDPT2, is reported. For the DF/CD-QDPT2 methods, the Hose-Kaldor approach is used. The DF-QDPT2 method, with the cc-pwCVTZ basis set, dramatically reduces the computational cost compared to conventional multiconfigurational QDPT2 (MC-QDPT2, from the Gamess 2017.R2 package), with a more than 122-fold reduction for the largest member of the diradical test set considered. The DF approximation enables substantially accelerated energies to be obtained for the QDPT2 approach due to the significantly reduced I/O time. The performance of the DF-QDPT2 and CD-QDPT2 methods is compared with that of CASSCF, the multireference second-order perturbation theory (MRMP2), MC-QDPT2, and CASSCF-based second-order perturbation theory (CASPT2) methods for singlet-triplet energy splitting (EST) in O2 and C2 molecules and for the dissociation energy of F2. For the O2 and C2 molecules, the performance of the DF-QDPT2 and CD-QDPT2 methods is significantly better than that of CASSCF, MRMP2, MC-QDPT2, and CASPT2; while for the F2 case, the results of DF-QDPT2, CD-QDPT2, MRMP2, MC-QDPT2, and CASPT2 are similar and remarkably better than that of CASSCF, which fails dramatically. Moreover, the DF-QDPT2, CASSCF, CASPT2, and MRCI+Q methods are applied to potential energy curves (PECs) for N2, CH4, and F2 molecules. Our results demonstrate that the performance of DF-QDPT2 is substantially better than that of CASSCF and is comparable with that of CASPT2 for the molecules considered. Overall, the present application results demonstrate that the DF-QDPT2 and CD-QDPT2 methods are very promising for electronically challenging molecular systems suffering from (quasi)degeneracy problems, where the single-reference methods cannot provide an accurate electronic description, but the DF-QDPT2 and CD-QDPT2 methods can do so at significantly reduced computational costs.

Electronic Communication between S=1/2 Spins in Negatively-charged Double-caged Fullerene C60 Derivative Bonded by Two Single Bonds and Pyrrolizidine Bridge.

Radical anion salt {cryptand[2.2.2] (K+ )}2 (bispheroid)2- ⋅3.5C6 H4 Cl2 (1) of the double-caged fullerene C60 derivative, in which fullerene cages are linked by a cyclobutane bridging cycle and additionally by a pyrrolizidine moiety, was obtained. Each fullerene cage in this derivative accepts one electron on reduction, thus forming the (bispheroid)2- dianions with two interacting S=1/2 spins on the neighboring cages. Low-temperature magnetic measurements reveal a singlet ground state of the bispheroid dianions whereas triplet contributions prevail at increased temperature. An estimated exchange interaction between two spins J/kB =-78 K in 1 indicates strong magnetic coupling between them, nearly two times higher than that (J/kB =-44.7 K) in previously studied (C60 - )2 dimers linked via a cyclobutane bridge only. The enhancement of magnetic coupling in 1 can be explained by a shorter distance between the fullerene cages and, possibly, an additional channel for the magnetic exchange provided by a pyrrolizidine bridge. Quantum-chemical calculations of the lowest electronic state of the dianions by means of multi-configuration quasi-degenerate perturbation theory support the experimental findings.

A generalized vibronic-coupling Hamiltonian for molecules without symmetry: Application to the photoisomerization of benzopyran.

We present a model for the lowest two potential energy surfaces (PESs) that describe the photoinduced ring-opening reaction of benzopyran taken as a model compound to study the photochromic ring-opening reaction of indolinobenzospiropyran and its evolution toward its open-chain analog. The PESs are expressed in terms of three effective rectilinear coordinates. One corresponds to the direction between the equilibrium geometry in the electronic ground state, referred to as the Franck-Condon geometry, and the minimum of conical intersection (CI), while the other two span the two-dimensional branching space at the CI. The model correctly reproduces the topography of the PESs. The ab initio calculations are performed with the extended multiconfiguration quasidegenerate perturbation theory at second order method. We demonstrate that accounting for electron dynamic correlation drastically changes the global energy landscape since some zwitterionic states become strongly stabilized. Quantum dynamics calculations using this PES model produce an absorption spectrum that matches the experimental one to a good accuracy.

Spin-dependent properties in the framework of the dynamic correlation dressed complete active space method.

We report an extension of the recently proposed 2nd order dynamic correlation dressed complete active space method [S. Pathak et al., J. Chem. Phys. 147, 234109 (2017)] to incorporate spin-dependent relativistic effects into the Hamiltonian. The result is an effective Hamiltonian that contains the effects of static correlation, dynamic correlation, and relativistic effects on an equal footing. All contributions necessary for the description of magnetic phenomena and electron paramagnetic resonance (EPR) spectroscopy, namely, spin-orbit coupling, magnetic hyperfine coupling, Zeeman interaction, and direct electronic spin-spin coupling, are incorporated. We also suggest a novel analysis of g-matrices and A-matrices based on the singular value decomposition, which can provide not only the magnitude but also the sign of the principal components and allows for a transparent decomposition into different physical contributions. The new method was tested for excitation energies of first-row transition metal ions as well as D-tensors and g-shifts of first-row transition metal complexes using minimal active spaces. It was observed that state-mixing effects are usually small in these cases and that the results are comparable to nondegenerate N-electron valence state perturbation theory (NEVPT2) in conjunction with quasi-degenerate perturbation theory (QDPT). Results on EPR parameters of pseudo-square-planar Cu(ii) complexes show that state-mixing with a ligand-to-metal-charge-transfer configuration greatly improves results compared with NEVPT2/QDPT but also demonstrate that future modifications of the 0th order Hamiltonian or more elaborate electron correlation treatments will be necessary in order to achieve better agreement with the experiment.

Anharmonic Vibrational Analysis of Biomolecules and Solvated Molecules Using Hybrid QM/MM Computations.

Quantum mechanics/molecular mechanics (QM/MM) calculations are applied for anharmonic vibrational analyses of biomolecules and solvated molecules. The QM/MM method is implemented into a molecular dynamics (MD) program, GENESIS, by interfacing with external electronic structure programs. Following the geometry optimization and the harmonic normal-mode analysis based on a partial Hessian, the anharmonic potential energy surface (PES) is generated from QM/MM energies and gradients calculated at grid points. The PES is used for vibrational self-consistent field (VSCF) and post-VSCF calculations to compute the vibrational spectrum. The method is first applied to a phosphate ion in solution. With both the ion and neighboring water molecules taken as a QM region, IR spectra of representative hydration structures are calculated by the second-order vibrational quasi-degenerate perturbation theory (VQDPT2) at the level of B3LYP/cc-pVTZ and TIP3P force field. A weight-average of IR spectra over the structures reproduces the experimental spectrum with a mean absolute deviation of 16 cm–1. Then, the method is applied to an enzyme, P450 nitric oxide reductase (P450nor), with the NO molecule bound to a ferric (FeIII) heme. Starting from snapshot structures obtained from MD simulations of P450nor in solution, QM/MM calculations have been carried out at the level of B3LYP-D3/def2-SVP(D). The spin state of FeIII(NO) is likely a closed-shell singlet state based on a ratio of N–O and Fe–NO stretching frequencies (νN–O and νFe–NO) calculated for closed- and open-shell singlet states. The calculated νN–O and νFe–NO overestimate the experimental ones by 120 and 75 cm–1, respectively. The electronic structure and solvation of FeIII(NO) affect the structure around the heme of P450nor leading to an increase in νN–O and νFe–NO.

Polarizability of electronically excited molecular oxygen: theory and experiment

Multireference ab initio calculations (by using the extended multiconfiguration quasi-degenerate second-order perturbation theory method XMCQDPT2) have been employed to determine the static polarizabilities for the ground triplet () and two excited singlet (a1Δg and ) electronic states of molecular oxygen. The corrections to polarizabilities for the nuclear zero point motion are also reported. It was revealed that the excitation of an O2 molecule into the lowest singlet electronic states leads to a decrease in its polarizability: the polarizabilities of O2(a1Δg) and O2() are smaller (by factors of 0.967 and 0.962, respectively) than that of O2(). The theoretical results for the state were quantitatively confirmed experimentally employing the diffraction at laser-induced gratings.

Ab initio investigation of Br-3d core-excited states in HBr and HBr+ toward XUV probing of photochemical dynamics.

Ultrafast X-ray/XUV transient absorption spectroscopy is a powerful tool for real-time probing of chemical dynamics. Interpretation of the transient absorption spectra requires knowledge of core-excited potentials, which necessitates assistance from high-level electronic-structure computations. In this study, we investigate Br-3d core-excited electronic structures of hydrogen bromide (HBr) using spin-orbit general multiconfigurational quasidegenerate perturbation theory (SO-GMC-QDPT). Potential energy curves and transition dipole moments are calculated from the Franck-Condon region to the asymptotic limit and used to construct core-to-valence absorption strengths for five electronic states of HBr () and two electronic states of HBr+ (2Π3∕2, 2Σ1∕2). The results illustrate the capabilities of Br-3d edge probing to capture transitions of the electronic-state symmetry as well as nonadiabatic dissociation processes that evolve across avoided crossings. Furthermore, core-to-valence absorption spectra are simulated from the neutral state and the ionic states by numerically solving the time-dependent Schrödinger equation and exhibit excellent agreement with the experimental spectrum. The comprehensive and quantitative picture of the core-excited states obtained in this work allows for transparent analysis of the core-to-valence absorption signals, filling gaps in the theoretical understanding of the Br-3d transient absorption spectra.

State-interaction pair density functional theory for locally avoided crossings of potential energy surfaces in methylamine.

The strong couplings between electronic states in conical intersection regions are among the most challenging problems in quantum chemistry. XMS-CASPT2, a second-order multireference quasidegenerate perturbation theory, has been successful in describing potential energy surfaces near the conical intersections. We have recently proposed a less expensive method for this problem, namely state-interaction pair-density functional theory (SI-PDFT), which considers the coupling between electronic states described by multiconfiguration pair-density functional theory (MC-PDFT). Here we test the accuracy of SI-PDFT for closely coupled potential energy surfaces of methylamine along five different reaction paths for N-H bond fission. We choose paths that pass close to a conical intersection of the ground and first excited states. We find that SI-PDFT predicts potential energy curves and energy splittings near the locally avoided crossing in close proximity to those obtained by XMS-CASPT2. This validates the method for application to photochemical simulations.

Potential functions of internal rotation of the methacryloyl fluoride molecule in the ground (S0) and excited (S1) electronic states

The potential functions of internal rotation V(φ) (PFIR) of methacryloyl fluoride (MAF) in the ground (S0) and excited (S1) electronic states were reconstructed using the TORSIO program from experimental energy levels of the torsional transitions in the s-trans- and s-cis isomers. The energy levels were obtained from the analysis of the vibrational structure in the high-resolution gas-phase UV spectrum. The (S0) and (S1) equilibrium geometries of the s-trans- and s-cis rotational isomers of MAF as well as structural parameters for a set of points along the relaxed geometry scans, which were used to find expansion coefficients of kinematic function F(φ) in the Fourier series, were calculated using extended multiconfiguration quasi-degenerate perturbation theory, XMCQDPT2/SA(2)-CASSCF(6,5)/aug-cc-pVTZ. The ground (S0) state calculations were also done at the MP2 level of theory. In (S0) state, parameters Vn., barriers of internal rotation ΔH‡ and ΔH of MAF isomers were calculated using two theories. The calculated values of Vn, ΔH‡, ΔH in (S0) state are in good agreement with those derived from the vibrationally resolved UV spectrum of MAF in the gas phase. Within the one-dimensional model, the experimentally derived barrier heights that hinder internal rotation in MAF were found to be 2100 ± 50 cm−1 and 4950 ± 250 cm−1 in the (S0) and (S1) states, respectively. The parameters Vn and ΔH‡ in (S1) state are determined for first time.

Modeling structure and excitation of biliverdin-binding domains in infrared fluorescent proteins

We characterize structures and electronic excitation of domains from a bacteriophytochrome-based infrared fluorescent protein carrying a covalently bound biliverdin chromophore using the quantum mechanics/molecular mechanics methods. We show that geometry optimization at the density functional theory level and application of the extended multiconfigurational quasidegenerate perturbation theory in quantum subsystems allows us to achieve high calculation accuracy for the model systems mimicking the red-adsorbing and the far-red-adsorbing protein forms. Specifically, discrepancies between experimental and theoretical excitation energies are less than 0.05 eV (∼20 nm) for the Q-band in both protein forms.