Excited States of Conjugated Hydrocarbons Using the Molecular Mechanics - Valence Bond (MMVB) Method: Conical Intersections and Dynamics

We developed the molecular mechanics—valence bond (MMVB) method following an original suggestion of Jean-Paul Malrieu and coworkers. By coupling a parameterized Heisenberg Hamiltonian to a standard classical force field (MM2), reliable ground and excited state geometries of conjugated hydrocarbons can be rapidly optimized. The MMVB method was central to our development of algorithms for locating conical intersections and calculating their associated decay dynamics. Here, we briefly review the chemical applications of MMVB to date, and present two new studies using the photostability of pyracylene and the excited state decay dynamics of the photochromic dihydroazulene/vinylheptafulvene (DHA/VHF) reaction.     

Molecular mechanics-valence bond method for planar conjugated hydrocarbon cations

We present an extension of the molecular mechanics-valence bond (MMVB) hybrid method to study ground and excited states of planar conjugated hydrocarbon cations. Currently, accurate excited state calculations on these systems are limited to expensive ab initio studies of smaller systems: up to 15 active electrons in 16 pi orbitals with complete active space self-consistent field (CASSCF) theory using high symmetry. The new MMVB extension provides a faster, cheaper treatment to investigate larger cation systems with more than 24 active orbitals. Extension requires both new matrix elements and new parameters: In this paper we present both, for the limited planar case. The scheme is tested for the planar radical cations of benzene, naphthalene, anthracene, and phenanthrene. Calculated MMVB relative energies are in good agreement with CASSCF results for equilibrium geometries on the ground and first excited states, and conical intersections.     

Perturbative correction for the basis set incompleteness error of complete-active-space self-consistent field

To reduce the basis set incompleteness of the complete-active-space self-consistent field (CASSCF) wave function and energy we develop a second-order perturbation correction due to single excitations to complete set of unoccupied states. Other than the one- and two-electron integrals, only one- and two-particle reduced density matrices are required to compute the correction, denoted as [2](S). Benchmark calculations on prototypical ground-state bond-breaking problems show that only the aug-cc-pVXZ basis is needed with the [2](S) correction to match the accuracy of CASSCF energies of the aug-cc-pV(X+1)Z quality.     

Molecular mechanics force-field development for amino acid zwitterions

Understanding the conformational flexibility of amino acid zwitterions (ZWs) and their associated conformational energies is crucial for predicting their interactions in biological systems. Gas-phase ab initio calculations of ZWs are intractable. Molecular mechanics (MM), on the other hand, is able to handle large systems but lacks the necessary force field parameters to model ZWs. To develop force field parameters that are able to correctly model ZW geometries and energetics we used a novel combinatorial approach: amino acid ZWs were broken down structurally into key functional components, which were parameterized separately. M?ller-Plesset second-order perturbation calculations on small carboxylates, on the glycine cation, and on novel hydrogen bonded systems, coupled with available experimental data, were used to generate MM3(2000) ZW parameters (Allinger N. L.; Yuh, Y. H.; Lii, J.-H. J Am Chem Soc 1989, 111, 8551). The MM3 results from this combinatorial approach gave geometries that are in good agreement with neutron diffraction experiments, plus their frequencies and energies appear to be reasonably modeled. Current limitations and future development of MM force fields are discussed briefly.     

Photostability via sloped conical intersections: a computational study of the pyrene radical cation

The photophysics of the pyrene radical cation, a polycyclic aromatic hydrocarbon (PAH) and a possible source of diffuse interstellar bands (DIBs), is investigated by means of hybrid molecular mechanics-valence bond (MMVB) force field and multiconfigurational CASSCF and CASPT2 ab initio methods. Potential energy surfaces of the first three electronic states D 0, D 1, and D 2 are calculated. MMVB geometry optimizations are carried out for the first time on a cationic system; the results show good agreement with CASSCF optimized structures, for minima and conical intersections, and errors in the energy gaps are no larger than those found in our previous studies of neutral systems. The presence of two easily accessible sloped D 1/D 2 and D 0/D 1 conical intersections suggests the pyrene radical cation is highly photostable, with ultrafast nonradiative decay back to the initial ground state geometry predicted via a mechanism similar to the one found in the naphthalene radical cation.     

A study of the correlation effects upon the modelization of the double exchange phenomenon

A previous work by the authors has shown that the usual spin Hamiltonian used to model the magnetic spectra of mixed valence compounds was not sufficient to reproduce the magnetic spectrum of the molecule [Fe(2)(OH)(3)(NH(3))(6)](2+). In the present paper, the spin Hamiltonian is confronted to correlated ab initio calculations. The discrepancy between this Hamiltonian and the calculations is investigated and explained. It is pointed out that the multiconfigurational nature of the transition metal is responsible for this discrepancy. However, we show that this effect can easily be treated at the complete active space self-consistent field (CASSCF) level and that no further correlation treatment is needed. The spin Hamiltonian, which reproduces very well the minimal CASSCF results, could not be improved to recover the multireference effects.     

The reaction OH + C2H4: an example of rotational channel switching

The low-temperature data for the reaction between OH and C(2)H(4) is treated canonically as either a two-well or one-well problem using the "Multiwell" suite of codes, in which a "well" refers to a minimum in the potential energy surface. The former is analogous to the two transition state model of Greenwald et al. [Greenwald, E. E.; North, S. W.; Georgievskii, Y.; Klippenstein, S. J. J. Phys. Chem. A2005, 109, 6031], while the latter reflects the dominance of the so-called "inner transition state". External rotations are treated adiabatically, causing changes in the magnitude of effective barriers as a function of temperature. Extant data are well-described with either model using only the average energy transferred in a downward direction, upon collision, ΔE(d)(T), as a fitting parameter. The best value for the parameters describing the rate coefficient as a function of temperature (200 < T/K < 400) (Data at lower temperature is too sparse to yield a recommendation.) and pressure in the form used in the NASA/JPL format [Sander, S. P.; Abbatt, J.; Barker, J. R.; Burkholder, J. B.; Friedl, R. R.; Golden, D. M.; Huie, R. E.; Kolb, C. E.; Kurylo, M. J.; Moortgat, G. K et al., Chemical Kinetics and Photochemical Data for Use in Atmospheric Studies, Evaluation Number 17, Jet Propulsion Laboratory, 2011] are k(0) = 1.0 × 10(-28)(T/300)(-3.5) cm(6) molecule(-2) s(-1) and k(∞) to 8.0 × 10(-12)(T/300)(-2.3) cm(3) molecule(-1) s(-1).     

Calculations of molecular properties in hybrid coupled-cluster and molecular mechanics approach

We report benchmark calculations obtained with our new coupled-cluster singles and doubles (CCSD) code for calculating the first- and second-order molecular properties. This code can be easily incorporated into combined [Valiev, M.; Kowalski, K. J. Chem. Phys. 2006, 125, 211101] classical molecular mechanics (MM) and ab initio coupled-cluster (CC) calculations using NWChem, enabling us to study molecular properties in a realistic environment. To test this methodology, we discuss the results of calculations of dipole moments and static polarizabilities for the Cl2O system in the CCl4 solution using the CCSD (CC with singles and doubles) linear response approach. We also discuss the application of the asymptotic extrapolation scheme (AES) [Kowalski, K.; Valiev, M. J. Phys. Chem. A 2006, 110, 13106] in reducing the numerical cost of CCSD calculations.     

Theoretical prediction of the S1-S0 internal conversion of 6-cyanoazulene

Ab initio complete active-space self-consistent field (CASSCF) and second-order Multireference M?ller-Plesset perturbation (MRMP2) calculations were performed to examine the S1-S0 internal conversion of 6-cyanoazulene (6CNAZ). The azulene skeletons of 6CNAZ in S0 and S1 have features that resemble those of azulene. The stable geometry in S0 is characterized by (i) a C2v structure, (ii) an aromatic bond-equalized structure in which all the peripheral skeletal bond distances resemble an aromatic CC bond distance, and (iii) a single bond character of the transannular bond. The stable geometry in S1 is characterized by a nonaromatic C2v structure. Contrary to similarities of the stable geometries in S0 and S1 between 6CNAZ and azulene, the conical intersection (S1/S0-CIX) of 6CNAZ is different from that of azulene. The S1/S0-CIX of 6CNAZ takes a planar structure, whereas that of azulene takes a nonplanar structure in the seven-membered ring (Amatatsu, Y.; Komura, K. J. Chem. Phys. 2006, 125, 174311/1-8). On the basis of those computational findings, we predict the photochemical behavior of 6CNAZ in the S1-S0 internal conversion.     

Photostability via a sloped conical intersection: a CASSCF and RASSCF study of pyracylene

An extensive ab initio study of the ground- and excited-state potential energy surfaces of pyracylene is presented in this work. CASSCF calculations show that there is an accessible sloped S0/S1 conical intersection, which leads to ultrafast internal conversion and explains the observed photostability. RASSCF calculations (using a well-defined subset of the CASSCF configurations) are shown to be able to reproduce CASSCF results satisfactorily and will therefore be useful for larger systems where CASSCF is currently too expensive. MRCI and MRPT2 energy corrections are computed to assess the ionic character of the excited states. Finally, MMVB calculations are also benchmarked against CASSCF, to assess the reliability of this parametrized method for excited states of large conjugated polycyclic aromatic hydrocarbons.     

New relativistic atomic natural orbital basis sets for lanthanide atoms with applications to the Ce diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are included as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.     

Reaction of ethylene with hydroxyl radicals: a theoretical study

Ab initio calculations of portions of the C2H5O potential energy surface critical to the title reaction are presented. These calculations are based on QCISD geometries and frequencies and RQCISD(T) energies extrapolated to the complete-basis-set limit. Rate coefficients for the reaction of C2H4 with OH are calculated using this surface and the two transition-state model of Greenwald and co-workers [J. Phys. Chem. A 2005, 109, 6031] for the association of OH with C2H4. The present calculations reproduce most of the experimental data, including the temperature and pressure dependence of the rate coefficients, with only a small (0.4 kcal/mol) adjustment to the energy barrier for direct hydrogen abstraction. We confirm the importance of this channel above 800 K and find that a significant fraction of the total rate coefficient (approximately 10%) is due to the formation of vinyl alcohol above this temperature. Calculations of the vinyl alcohol channel are consistent with the recent observation of this molecule in low-pressure flames [Taatjes, C. A.; Hansen, N.; McIlroy, A.; Miller, J. A.; Senosiain, J. P.; Klippenstein, S. J.; Qi, F.; Sheng, L.; Zhang, Y.; Cool, T. A.; Wang, J.; Westmoreland, P. R.; Law, M. E.; Kasper, T.; Kohse-H?inghaus, K. Science 2005, 308, 1887] and suggest that this reaction should be included in hydrocarbon oxidation mechanisms.     

Interprotein electron transfer in a confined space: uncoupling protein dynamics from electron transfer by sol-gel encapsulation

In this paper, we describe the first observations of photoinitiated interprotein electron transfer (ET) within sol-gels. We have encapsulated three protein-protein complexes, specifically selected because they represent a full range of affinities, are sensitive to different types of dynamic processes, and thus are expected to respond differently to sol-gel encapsulation. The three systems are (i) the [Zn, Fe(3+)L] mixed-metal hemoglobin hybrids, where the alpha(1)-Zn and beta(2)-Fe subunits correspond to a "predocked" protein-protein complex with a crystallographically defined interface (Natan, M. J.; Baxter, W. W.; Kuila, D.; Gingrich, D. J.; Martin, G. S.; Hoffman, B. M. Adv. Chem. Ser. 1991, 228 (Electron-Transfer Inorg., Org., Biol. Syst.), 201-213), (ii) the Zn-cytochrome c peroxidase complex with cytochrome c, [ZnCcP, Fe(3+)Cc], having an intermediate affinity between its partners (Nocek, J. M.; Zhou, J. S.; De Forest, S.; Priyadarshy, S.; Beratan, D. N.; Onuchic, J. N.; Hoffman, B. M. Chem. Rev. 1996, 96, 2459-2489), and (iii) the [Zn-deuteromyoglobin, ferricytochrome b(5)] complex, [ZnDMb, Fe(3+)b(5)], which is loosely bound and highly dynamic (Liang, Z.-X.; Nocek, J.; Huang, K.; Hayes, R. T.; Kurnikov, I. V.; Beratan, D. N.; Hoffman, B. M. J. Am. Chem. Soc. 2002, 124, 6849-6859. Intersubunit ET within the hybrid does not involve second-order processes or subunit rearrangements, and thus is influenced only by perturbations of high-frequency motions coupled to ET. For the latter two complexes, sol-gel encapsulation eliminates second-order processes: protein partners encapsulated as a complex must stay together throughout a photoinitiated ET cycle, while proteins encapsulated alone cannot acquire a partner. It further modulates intracomplex motions of the two partners.     

CASSCF and CASPT2 studies on the structures, transition energies, and dipole moments of ground and excited states for azulene

The electronic structure of azulene molecule has been studied. We have obtained the optimized structures of ground and singlet excited states by using the complete active space self-consistent-field (CASSCF) method, and calculated vertical and 0-0 transition energies between the ground and excited states with second-order M?ller-Plesset perturbation theory (CASPT2). The CASPT2 calculations indicate that the bond-equalized C(2v) structure is more stable than the bond-alternating C(s) structure in the ground state. For a physical understanding of electronic structure change from C(2v) to C(s), we have performed the CASSCF calculations of Duschinsky matrix describing mixing of the b(2) vibrational mode between the ground (1A(1)) and the first excited (1B(2)) states based on the Kekule-crossing model. The CASPT2 0-0 transition energies are in fairly good agreement with experimental results within 0.1-0.3 eV. The CASSCF oscillator strengths between the ground and excited states are calculated and compared with experimental data. Furthermore, we have calculated the CASPT2 dipole moments of ground and excited states, which show good agreement with experimental values.     

Unusual magnetic properties of mixed-valence system: multiconfigurational method theoretical study on Mn2+ cation

The geometry structure, dissociation energy, vibrational frequencies, and low-lying spin-state energy spectrum of Mn2+ are investigated by using ab initio CASSCF/ECP10MDF, complete active space self-consistent field/atomic natural orbital basis sets (CASSCF/ANO-s), CASPT2/ECP10MDF, and second-order perturbation theory with CASSCF reference function/atomic natural orbital basis sets (CASPT2/ANO-s) levels of theory. For the ground state the dissociation energy of 1.397 eV calculated at the CASPT2/ANO-s level supports Jarrlod's experimental value of 1.39 eV. The equilibrium bond length and vibrational frequency are 2.940 A calculated at the CASPT2/ANO-s level of theory and 214.4 cm-1 calculated at the CASSCF/ANO-s level of theory, respectively. On the basis of the mixed-valence model, the Heisenberg exchange constant J(-71.2 cm-1) and the double-exchange constant B(647.7 cm-1) are extracted explicitly from the low-lying energy spectrum calculated at the higher levels of theory. The magnetic competition between the weaker Heisenberg exchange interactions and the stronger double-exchange interactions makes the ground state a 12Sigmag+ state, consistent with electron paramagnetic resonance experimental observation, which explains unusual magnetic properties of Mn2+, quite different from the antiferromagnetic ground state of Mn2 and Cr2. On the other hand, the results calculated at the higher levels of theory show the consistent antiferromagnetic Heisenberg exchange interactions between 3d-3d for Cr2, Mn2+, and Mn2.     

The structure of acrolein in a liquid crystal phase

The (1)H NMR spectrum of a sample of acrolein dissolved in the nematic liquid crystal phase I52 has been analysed to yield 18 dipolar couplings between all the magnetic nuclei in the molecule; moreover, the (13)C and (13)C{(1)H} NMR spectra of a sample of acrolein in CDCl(3) were recorded and analysed to determine the indirect J(ij) couplings. The data were used to obtain the relative positions of the carbon and hydrogen atoms, assuming that these are independent of the conformations generated by rotation around the C--C bond through an angle phi, and to obtain a probability distribution P(phi). It has been found that in the liquid phase, the distribution is a maximum at the trans form whereas the abundance of the cis form is significantly smaller compared with that found by microwave spectroscopy or high level quantum mechanical calculations. Such calculations produced also a suitable force field needed to develop suitable strategies for vibrational correction procedure in the case of flexible molecules.     

A perturbation-based super-CI approach for the orbital optimization of a CASSCF wave function

A perturbation theory-based algorithm for the iterative orbital update in complete active space self-consistent-field (CASSCF) calculations is presented. Following Angeli et al. (J. Chem. Phys. 2002, 117, 10525), the first-order contribution of singly excited configurations to the CASSCF wave function is evaluated using the Dyall Hamiltonian for the determination of a zeroth-order Hamiltonian. These authors employ an iterative diagonalization of the first-order density matrix including the first-order correction arising from single excitations, whereas the present approach uses the single-excitation amplitudes directly for the construction of the exponential of an anti-Hermitian matrix resulting in a unitary matrix which can be used for the orbital update. At convergence, the single-excitation amplitudes vanish as a consequence of the generalized Brillouin's theorem. It is shown that this approach in combination with direct inversion of the iterative subspace (DIIS) leads to very rapid convergence of the CASSCF iteration procedure. © 2019 Wiley Periodicals, Inc.     

Theoretical studies for excited-state tautomerization in the 7-azaindole-(CH3OH)n (n = 1 and 2) complexes in the gas phase

The excited-state tautomerization of 7-azaindole (7AI) complexes bonded with either one or two methanol molecule(s) was studied by systematic quantum mechanical calculations in the gas phases. Electronic structures and energies for the reactant, transition state (TS), and product were computed at the complete active space self-consistent field (CASSCF) levels with the second-order multireference perturbation theory (MRPT2) to consider the dynamic electron correlation. The time-dependent density functional theory (TDDFT) was also used for comparison. The excited-state double proton transfer (ESDPT) in 7AI-CH(3)OH occurs in a concerted but asynchronous mechanism. Similarly, such paths are also found in the two transition states during the excited-state triple proton transfer (ESTPT) of the 7AI-(CH(3)OH)(2) complex. In the first TS, the pyrrole ring proton first migrated to methanol, while in the second the methanol proton moved first to the pyridine ring. The CASSCF level with the MRPT2 correction showed that the former path was much preferable to the latter, and the ESDPT is much slower than the ESTPT. Additionally, the vibrational-mode enhanced tautomerization in the 7AI-(CH(3)OH)(2) complex was also studied. We found that the excitation of the low-frequency mode shortens the reaction path to increase the tautomerization rate. Overall, most TDDFT methods used in this study predicted different TS structures and barriers from the CASSCF methods with MRPT2 corrections.     

Theoretical study of the energetics of the reactions of triplet dioxygen with hydroquinone, semiquinone, and their protonated forms: relation to the mechanism of superoxide generation in the respiratory chain

One-electron reduction of the dioxygen molecule by the reduced form of mitochondrial ubiquinones (Q) of the NADH dehydrogenase (complex I) and mitochondrial cytochrome bc1 (complex III) is believed to be the main source of the superoxide anion radical O2*- and the hydroperoxide radical OOH*. In this work, we modeled the energetics of four possible reactions of the triplet ((3)Sigma(g)) dioxygen-molecule reduction by fully reduced and protonated ubiquinone (QH2; reaction 1), its deprotonated form (QH-; reaction 2), the semiquinone radical (QH*; reaction 3), and the semiquinone anion radical (Q*-; reaction 4), by means of ab initio calculations with the 6-31G(d) and 6-31+G(d) basis set in the restricted open-shell Hartree-Fock (ROHF), unrestricted Hartree-Fock (UHF), and complete active space self-consistent field (CASSCF) with dynamic correlation [at the second-order M?ller-Plesset (MP2) or multiple reference M?ller-Plesset (MRMP), respectively] schemes and the basis set superposition error (BSSE) correction included, as well as semiempirical AM1 and PM3 calculations in the UHF and ROHF schemes. 2-Butene-1,4-dione and p-benzoquinone were selected as model compounds. For the reduced forms of both compounds, reaction 1 turned out to be energetically unfavorable at all levels of theory, this agreeing with the experimentally observed diminished reductive properties of hydroquinone derivatives at low pH. For 2-butene-1,4-dione treated at the most advanced MRMP/CASSCF/6-31+G(d) level, the energies of reactions 1-4 are 4.7, -34.3, -15.0, and -4.1 kcal/mol, respectively. This finding suggests that reactions 2 and 3 are the most likely mechanisms of electron transfer to molecular oxygen in aprotic environments and that proton transfer is involved in this process. Nearly the same energies of reactions 2 and 3 were calculated at the MRMP/CASSCF/6-31+G(d) level for reduced forms of p-benzoquinone. Inclusion of diffuse functions in the basis set and dynamic correlation at the CASSCF level appears essential. Because deprotonated ubiquinol is unlikely to exist in physiological environments, reaction 3 appears to be the most likely mechanism of one-electron reduction of oxygen; however, if oxygen can penetrate cytochrome bc1 as far as the Q(o) center where ubiquinol can be deprotonated, reaction 2 can also come into play. The energies of reactions 2 and 3 calculated at the MRMP/CASSCF/6-31+G(d) level are most closely reproduced in the ab initio and semiempirical UHF PM3 calculations. Additional semiempirical calculations on more realistic models of ubiquinone, 2,3-dimethoxy-6-methyl-p-benzoquinone and 2,3-dimethoxy-5-isoprenyl-6-methyl-p-benzoquinone, gave qualitatively the same relations between the energies of reactions 2 and 3 as those carried out for p-benzoquinone species, thereby suggesting that this method could be used in studying electron-transfer reactions from reduced quinone derivatives to molecular oxygen in more complex systems, such as a model of the Q(o) site of cytochrome bc1, where applying ab initio methods is unfeasible.