Mark R. Hoffmann

New Excited-State Proton Transfer Mechanisms for 1,8-Dihydroxydibenzo[a,h]phenazine

The excited state intramolecular proton transfer (ESIPT) mechanisms of 1,8-dihydroxydibenzo[a,h]phenazine (DHBP) in toluene solvent have been investigated based on time-dependent density functional theory (TD-DFT). The results suggest that both a single and double proton transfer mechanisms are relevant, in constrast to the prediction of a single one proposed previously (Piechowska et al. J. Phys. Chem. A 2014, 118, 144-151). The calculated results show that the intramolecular hydrogen bonds were formed in the S0 state, and upon excitation, the intramolecular hydrogen bonds between -OH group and pyridine-type nitrogen atom would be strengthened in the S1 state, which can facilitate the proton transfer process effectively. The calculated vertical excitation energies in the S0 and S1 states reproduce the experimental UV-vis absorption and fluorescence spectra well. The constructed potential energy surfaces of the S0 and S1 states have been used to explain the proton transfer process. Four minima have been found on the S1 state surface, with potential barriers between these excited-state minima of less than 10 kcal/mol, which supports concomitant single and double proton transfer mechanisms. In addition, the fluorescence quenching can be explained reasonably based on the proton transfer process.

Explication and revision of generalized Van Vleck perturbation theory for molecular electronic structure

A revision of second-order Generalized Van Vleck Perturbation Theory (GVVPT2) for the description of dynamic electron correlation in molecules is presented. It is shown that the basic formulas of the suggested method are well-defined approximations to the theoretically carefully constructed self-consistent quasidegenerate perturbation theory. Furthermore, it is shown that nonlinear responses to the perturbations can be obtained by explicit formulas. The revised GVVPT2 makes active use of the recently introduced concept of macroconfigurations, whereby vast numbers of null Hamiltonian matrix elements are prescreened with minimal computational cost and the remainders are organized for facile computation by Table-CI-like methodology. Moreover, use of macroconfigurations allows the efficient use of incomplete model spaces, which extends drastically the applicability of the method. Representative calculations on model systems studied previously with the original formulation show close agreement and on additional model systems show the wide applicability of the revised formulation.

Quantum algorithm for obtaining the energy spectrum of molecular systems

Simulating a quantum system is more efficient on a quantum computer than on a classical computer. The time required for solving the Schrödinger equation to obtain molecular energies has been demonstrated to scale polynomially with system size on a quantum computer, in contrast to the well-known result of exponential scaling on a classical computer. In this paper, we present a quantum algorithm to obtain the energy spectrum of molecular systems based on the multiconfigurational self-consistent field (MCSCF) wave function. By using a MCSCF wave function as the initial guess, the excited states are accessible. Entire potential energy surfaces of molecules can be studied more efficiently than if the simpler Hartree-Fock guess was employed. We show that a small increase of the MCSCF space can dramatically increase the success probability of the quantum algorithm, even in regions of the potential energy surface that are far from the equilibrium geometry. For the treatment of larger systems, a multi-reference configuration interaction approach is suggested. We demonstrate that such an algorithm can be used to obtain the energy spectrum of the water molecule.

A Paramagnetic Bonding Mechanism for Diatomics in Strong Magnetic Fields

Magnetically Bound At the macroscopic scale associated with daily life on Earth, magnetic attraction can seem fairly strong—think of the great loads moved by magnetized cranes. Microscopically, however, the field strengths attainable by human construction act as just a small perturbation on the Coulombic forces that bind atoms into molecules. Lange et al. (p. 327; see the Perspective by Schmelcher) used theoretical calculations to examine atomic behavior in environments very close to certain stars, where magnetic fields exceed those attainable on Earth by factors of 10,000 or more. The results predict a distinct type of chemical bonding in which spin-parallel hydrogen atoms or ground-state helium atoms are drawn together into pairs. At the enormous field strengths prevailing near stars, theory predicts a magnetically induced class of chemical bonding. Elementary chemistry distinguishes two kinds of strong bonds between atoms in molecules: the covalent bond, where bonding arises from valence electron pairs shared between neighboring atoms, and the ionic bond, where transfer of electrons from one atom to another leads to Coulombic attraction between the resulting ions. We present a third, distinct bonding mechanism: perpendicular paramagnetic bonding, generated by the stabilization of antibonding orbitals in their perpendicular orientation relative to an external magnetic field. In strong fields such as those present in the atmospheres of white dwarfs (on the order of 105 teslas) and other stellar objects, our calculations suggest that this mechanism underlies the strong bonding of H2 in the Σ3u+(1σg1σu*) triplet state and of He2 in the Σ1g+(1σg21σu*2) singlet state, as well as their preferred perpendicular orientation in the external field.

A state-selective quasidegenerate perturbation theory for the electronic structure of molecules

Abstract A state-selective quasidegenerate second-order perturbation theory for the determination of the electronic structure of polyatomic molecules is presented. The tenability of the method is demonstrated by calculations on several well-known “benchmark” molecules: H 2 O, using a double zeta (DZ) basis set; the singlet—triplet and singlet—singlet energy separations of DZP CH 2 ; the excited states of DZP CH + 2 ; and the dissociations of F 2 and N 2 , using larger than DZP bases. The new method utilizes information available at the conclusion of a complete active space self-consistent field (CASSCF) calculation and is shown to improve CASSCF results.

Comparative study of multireference perturbative theories for ground and excited states

Three recently developed multireference perturbation theories (PTs)-generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH(2) system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied. Both Møller-Plesset (MP) and Epstein-Nesbet partition are used for MCPT and SS-MRPT, while GVVPT uses MP partitioning. An important thrust in our comparative study is to ascertain the degree of interplay of dynamical and nondynamical correlation for both ground and excited states. The same basis set and the same set of orbitals are used in all calculations to keep artifactual differences away when comparing the results. Nonparallelity error is used as a measure of the performance of the respective theories. Significant differences among the three methods appear when an intruder state is present. Additionally, difficulties arise (a) in MCPT when the choice of a pivot determinant becomes problematic, and (b) in SS-MRPT when there are small coefficients of the model function and there is implicit division by these coefficients, which generates a potential instability of the solutions. Ways to alleviate these latter shortcomings are suggested.

A self-consistent version of quasidegenerate perturbation theory

A new quasidegenerate perturbation theory is developed that describes the interactions of electronic states of interest with energetically low-lying excited states variationally and with more high-lying excited states perturbatively. The states of interest, the low-lying excited states and the more high-lying excited states, define primary, secondary, and external subspaces, respectively. The task of determination of the lowest solutions of the full configuration interaction (CI) problem is shown to be equivalent to the task of searching iteratively for an optimal primary subspace within the model space spanned by the initial unperturbed primary and secondary states. It is also shown that the present approach, which we refer to as the self-consistent quasidegenerate perturbation theory (SC-QDPT), theoretically satisfies the following criteria: (1) it avoids instabilities due to intruder states; (2) it ensures the additivity of the energy for noninteracting subsystems; (3) the projection of the correlated ...

Third-order complete active space self-consistent field based generalized Van Vleck perturbation theory

Abstract A state-selective generalized Van Vleck perturbation theory (GVVPT), correct through third order, for the determination of the electronic structure of polyatomic molecules is presented. The method adapts Kirtmans GVVPT for use with complete active space self-consistent field (CASSCF), and orthogonal complement, zeroth-order many-electron functions. The tenability of the method is demonstrated by calculations on several well-known “benchmark” molecules: the Be atom, using a (12s5p1d)/[7s3pld] basis set, double zeta (DZ) H2O; 6-31GN NH2; the singlet—triplet and singlet—singlet energy separations of DZP CH2; the excited states of DZP CH+2; and the dissociation of DZP + F2.

Configuration-driven unitary group approach for generalized Van Vleck variant multireference perturbation theory.

A new, efficient, configuration-driven algorithm utilizing the unitary group approach (UGA) was developed and implemented for the generalized van Vleck perturbation theory (GVVPT) variant of multireference perturbation theory. The computational speed has been improved by 1 or 2 orders of magnitude compared to the previous implementation based on the Table-CI technique. It is shown that the reformulation is applicable to both the second-order (GVVPT2) and third-order (GVVPT3) approximations. Calculations on model problems and on a chemically realistic description of cyclobutadiene are used to illustrate the performance of the method. The calculations on cyclobutadiene, using over 2.3 billion CSFs, provide results on geometric parameters and the barrier height of the automerization reaction in good agreement with established high accuracy results.

Embedding theory for excited states

Using the technique of Perdew and Levy [Phys. Rev. B 31, 6264 (1985)], it is shown that both the density function theory (DFT)-in-DFT and wave function theory (WFT)-in-DFT embedding approaches are formally correct in studying not only the ground state but also a subset of the excited states of the total system. Without further approximations, the DFT-in-DFT embedding approach results in a pair of coupled Euler-Lagrange equations. In contrast to DFT-in-DFT, the WFT-in-DFT approach is shown to ensure a systematic description of excited states if such states are mainly related to excitations within the embedded subsystem. Possible ways for the practical realization of the WFT-in-DFT approach for studying excited states are briefly discussed.