Christine A. Schwerdtfeger

Nonadiabatic Dynamics of Photoinduced Proton-Coupled Electron Transfer in a Solvated Phenol–Amine Complex

Photoinduced concerted electron-proton transfer (EPT), denoted photo-EPT, is important for a wide range of energy conversion processes. Transient absorption and Raman spectroscopy experiments on the hydrogen-bonded p-nitrophenylphenol-t-butylamine complex, solvated in 1,2-dichloroethane, suggested that this complex may undergo photo-EPT. The experiments probed two excited electronic states that were interpreted as an intramolecular charge transfer (ICT) state and an EPT state. Herein mixed quantum mechanical/molecular mechanical nonadiabatic surface hopping dynamics is used to investigate the relaxation pathways following photoexcitation. The potential energy surface is generated on the fly with a semiempirical floating occupation molecular orbital complete active space configuration interaction method for the solute molecule and a molecular mechanical force field for the explicit solvent molecules. The free energy curves along the proton transfer coordinate illustrate that proton transfer is thermodynamically and kinetically favorable on the lower-energy excited state but not on the higher-energy excited state, supporting the characterization of these states as EPT and ICT, respectively. The nonadiabatic dynamics simulations indicate that the population decays from the ICT state to the EPT state in ∼100 fs and from the EPT state to the ground state on the slower time scale of ∼1 ps, qualitatively consistent with the experimental measurements. For ∼54% of the trajectories, the proton transfers from the phenol to the amine in ∼400 fs on the EPT state and then transfers back to the phenol rapidly upon decay to the ground state. Thus, these calculations augment the original interpretation of the experimental data by providing evidence of proton transfer on the EPT state prior to decay to the ground state. The fundamental insights obtained from these simulations are also relevant to other photo-EPT processes.

Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene

Recently, parameterization of the two-electron reduced density matrix (2-RDM) has made possible the determination of electronic energies with greater accuracy and lower cost than traditional electron-pair theories including coupled cluster with single and double excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. We examine the methods performance for strongly correlated barriers to rotation; in particular, we study two distinct pathways in the isomerization of diazene (N(2)H(2)) from cis to trans: (i) a strongly correlated rotational pathway and (ii) a moderately correlated inversion pathway. While single reference wavefunction methods predict that the rotational barrier is higher than the inversional barrier, the parametric 2-RDM method predicts that the rotational barrier is lower than the inversional barrier by 3.1 kcal/mol in the extrapolated basis set limit. The parametric 2-RDM results are in agreement with those from multireference methods including multireference perturbation theory and the solution to the anti-Hermitian contracted Schrödinger equation. We report energies, optimized structures, and natural orbital occupation numbers for three diazene minima and two transition states.

Charge-dependent cavity radii for an accurate dielectric continuum model of solvation with emphasis on ions: aqueous solutes with oxo, hydroxo, amino, methyl, chloro, bromo, and fluoro functionalities.

Dielectric continuum solvation models are widely used because they are a computationally efficacious way to simulate equilibrium properties of solutes. With advances that allow for molecular-shaped cavities, they have reached a high level of accuracy, in particular for neutral solutes. However, benchmark tests show that existing schemes for defining cavities are unable to consistently predict accurately the effects of solvation on ions, especially anions. This work involves the further development of a protocol put forth earlier for defining the cavities of aqueous solutes, with resulting advances that are most striking for anions. Molecular cavities are defined as interlocked spheres around atoms or groups of atoms in the solute, but the sphere radii are determined by simple empirically based expressions involving the effective atomic charges of the solute atoms (derived from molecular electrostatic potential) and base radii. Both of these terms are optimized for the different types of atoms or functional groups in a training set of neutral and charged solutes. Parameters in these expressions for radii were fitted by minimizing residuals between calculated and measured standard free energies of solvation (DeltaG(s)*), weighted by the uncertainty in the measured value. The calculations were performed using density functional theory with the B3LYP functional and the 6-311+G** basis set and the COnductor-like Screening MOdel (COSMO). The optimized radii definitions reproduce DeltaG(s)* of neutral solutes and singly charged ions in the training set to within experimental uncertainty and, more importantly, accurately predict DeltaG(s)* of compounds outside the training set, in particular anions (J. Phys. Chem. A 2003, 107, 5778). Inherent to this approach, the cavity definitions reflect the strength of specific solute-water interactions. We surmise that this feature underlies the success of the model, referred to as the CD-COSMO model for Charge-Dependent (also Camaioni-Dupuis) COSMO model. These findings offer encouragement that we can keep extending this scheme to other functional groups and obtain better accuracy in using continuum solvation models to predict equilibrium properties of aqueous ionic solutes. The approach is illustrated for a number of test cases, including the determination of acidities of an amine base, a study of the tautomerization equilibrium of a zwitterionic molecule (glycine), and calculating solvation energies of transition states toward a full characterization of reaction pathways in aqueous phase, here in S(N)2 exchange reactions. The calculated reaction barriers in aqueous solution are in excellent agreement with experimental values.

Nonadiabatic dynamics of electron transfer in solution: Explicit and implicit solvent treatments that include multiple relaxation time scales

The development of efficient theoretical methods for describing electron transfer (ET) reactions in condensed phases is important for a variety of chemical and biological applications. Previously, dynamical dielectric continuum theory was used to derive Langevin equations for a single collective solvent coordinate describing ET in a polar solvent. In this theory, the parameters are directly related to the physical properties of the system and can be determined from experimental data or explicit molecular dynamics simulations. Herein, we combine these Langevin equations with surface hopping nonadiabatic dynamics methods to calculate the rate constants for thermal ET reactions in polar solvents for a wide range of electronic couplings and reaction free energies. Comparison of explicit and implicit solvent calculations illustrates that the mapping from explicit to implicit solvent models is valid even for solvents exhibiting complex relaxation behavior with multiple relaxation time scales and a short-time inertial response. The rate constants calculated for implicit solvent models with a single solvent relaxation time scale corresponding to water, acetonitrile, and methanol agree well with analytical theories in the Golden rule and solvent-controlled regimes, as well as in the intermediate regime. The implicit solvent models with two relaxation time scales are in qualitative agreement with the analytical theories but quantitatively overestimate the rate constants compared to these theories. Analysis of these simulations elucidates the importance of multiple relaxation time scales and the inertial component of the solvent response, as well as potential shortcomings of the analytical theories based on single time scale solvent relaxation models. This implicit solvent approach will enable the simulation of a wide range of ET reactions via the stochastic dynamics of a single collective solvent coordinate with parameters that are relevant to experimentally accessible systems.

Testing the parametric two-electron reduced-density-matrix method with improved functionals: Application to the conversion of hydrogen peroxide to oxywater

Parametrization of the two-electron reduced density matrix (2-RDM) has recently enabled the direct calculation of electronic energies and 2-RDMs at the computational cost of configuration interaction with single and double excitations. While the original Kollmar energy functional yields energies slightly better than those from coupled cluster with single-double excitations, a general family of energy functionals has recently been developed whose energies approach those from coupled cluster with triple excitations [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. In this paper we test the parametric 2-RDM method with one of these improved functionals through its application to the conversion of hydrogen peroxide to oxywater. Previous work has predicted the barrier from oxywater to hydrogen peroxide with zero-point energy correction to be 3.3-to-3.9 kcal/mol from coupled cluster with perturbative triple excitations [CCSD(T)] and -2.3 kcal/mol from complete active-space second-order perturbation theory (CASPT2) in augmented polarized triple-zeta basis sets. Using a larger basis set than previously employed for this reaction-an augmented polarized quadruple-zeta basis set (aug-cc-pVQZ)-with extrapolation to the complete basis-set limit, we examined the barrier with two parametric 2-RDM methods and three coupled cluster methods. In the basis-set limit the M parametric 2-RDM method predicts an activation energy of 2.1 kcal/mol while the CCSD(T) barrier becomes 4.2 kcal/mol. The dissociation energy of hydrogen peroxide to hydroxyl radicals is also compared to the activation energy for oxywater formation. We report energies, optimal geometries, dipole moments, and natural occupation numbers. Computed 2-RDMs nearly satisfy necessary N-representability conditions.

Populations of carbonic acid isomers at 210 K from a fast two-electron reduced-density matrix theory.

Parametrization of the 2-electron reduced density matrix (2-RDM) rather than the many-electron wave function yields a new family of electronic-structure methods that are faster and more accurate than traditional coupled electron-pair methods including coupled cluster with single and double excitations. Deriving the parametrization from N-representability conditions generates a 2-RDM that captures significant correlation from triple and higher-order excitations at the cost of double excitations. We apply the parametric 2-RDM method to confirm recent experiments determining the relative thermodynamic populations of the cis-cis and cis-trans isomers of carbonic acid. In 2010 Bernard et al. showed by infrared spectroscopy that the populations of cis-cis and cis-trans isomers have a 10:1 ratio at 210 K. By use of the parametric 2-RDM method, we predict a 8:1 ratio at 210 K. Comparable ab initio methods overestimate the stability of the cis-cis isomer with 24:1 and 21:1 ratios. These 2-RDM-based methods promise to have significant applications throughout chemistry.

Proton Quantization and Vibrational Relaxation in Nonadiabatic Dynamics of Photoinduced Proton-Coupled Electron Transfer in a Solvated Phenol-Amine Complex.

Nonadiabatic dynamics simulations of photoinduced proton-coupled electron transfer (PCET) in a phenol-amine complex in solution were performed. The electronic potential energy surfaces were generated on-the-fly with a hybrid quantum mechanical/molecular mechanical approach that described the solute with a multiconfigurational method in a bath of explicit solvent molecules. The transferring hydrogen nucleus was represented as a quantum mechanical wave function calculated with grid-based methods, and surface hopping trajectories were propagated on the adiabatic electron-proton vibronic surfaces. Following photoexcitation to the excited S1 electronic state, the overall decay to the ground vibronic state was found to be comprised of relatively fast decay from a lower proton vibrational state of S1 to a highly excited proton vibrational state of the ground S0 electronic state, followed by vibrational relaxation within the S0 state. Proton transfer can occur either on the highly excited proton vibrational states of S0 due to small environmental fluctuations that shift the delocalized vibrational wave functions or on the low-energy proton vibrational states of S1 due to solvent reorganization that alters the asymmetry of the proton potential and reduces the proton transfer barrier. The isotope effect arising from replacing the transferring hydrogen with deuterium is predicted to be negligible because hydrogen and deuterium behave similarly in both types of proton transfer processes. Although an isotope effect could be observed for other systems, in general the absence of an isotope effect does not imply the absence of proton transfer in photoinduced PCET systems. This computational approach is applicable to a wide range of other photoinduced PCET processes.

Relative energies and geometries of the cis- and trans-HO3 radicals from the parametric 2-electron density matrix method.

The parametric 2-electron reduced density matrix (2-RDM) method employing the M functional [Mazziotti, D. A. Phys. Rev. Lett. 2008, 101, 253002], also known as the 2-RDM(M) method, improves on the accuracy of coupled electron-pair theories including coupled cluster with single-double excitations at the computational cost of configuration interaction with single-double excitations. The cis- and trans-HO(3) isomers along with their isomerization transition state were examined using the recent extension of 2-RDM(M) to nonsinglet open-shell states [Schwerdtfeger, C. A.; Mazziotti, D. A. J. Chem. Phys. 2012, 137, 034107] and several coupled cluster methods. We report the calculated energies, geometries, natural-orbital occupation numbers, and reaction barriers for the HO(3) isomers. We find that the 2-RDM(M) method predicts that the trans isomer of HO(3) is lower in energy than the cis isomer by 1.71 kcal/mol in the correlation-consistent polarized valence quadruple-ζ (cc-pVQZ) basis set and 1.84 kcal/mol in the augmented correlation-consistent polarized valence quadruple-ζ (aug-cc-pVQZ) basis set. Results include the harmonic zero-point vibrational energies calculated in the correlation-consistent polarized valence double-ζ basis set. On the basis of the results of a geometry optimization in the augmented correlation consistent polarized valence triple-ζ basis set, the parametric 2-RDM(M) method predicts a central oxygen-oxygen bond of 1.6187 Å. We compare these energies and geometries to those predicted by three single-reference coupled cluster methods and experimental results and find that the inclusion of multireference correlation is important to describe properly the relative energies of the cis- and trans-HO(3) isomers and improve agreement with experimental geometries.

The tensor hypercontracted parametric reduced density matrix algorithm: Coupled-cluster accuracy with O(r4) scaling

Tensor hypercontraction is a method that allows the representation of a high-rank tensor as a product of lower-rank tensors. In this paper, we show how tensor hypercontraction can be applied to both the electron repulsion integral tensor and the two-particle excitation amplitudes used in the parametric 2-electron reduced density matrix (p2RDM) algorithm. Because only O(r) auxiliary functions are needed in both of these approximations, our overall algorithm can be shown to scale as O(r(4)), where r is the number of single-particle basis functions. We apply our algorithm to several small molecules, hydrogen chains, and alkanes to demonstrate its low formal scaling and practical utility. Provided we use enough auxiliary functions, we obtain accuracy similar to that of the standard p2RDM algorithm, somewhere between that of CCSD and CCSD(T).

Isoelectronic analogue of oxywater: a parametric two-electron reduced-density-matrix study of ammonia oxide

A parametrization of the two-electron reduced density matrix (2-RDM) provides energies that improve on the accuracy of coupled electron-pair theories including coupled cluster with single-double excitations at the computational cost of configuration interaction with single-double excitations [Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)]. This parametric 2-RDM method was recently employed to study the isomerization of oxywater to hydrogen peroxide where it predicted a lower energy barrier from oxywater (2.1 kcal mol−1) than coupled cluster methods (4.2 kcal mol−1). In this paper we study an isoelectronic analogue, the isomerization of ammonia oxide to hydroxylamine. In the extrapolated basis-set limit, using the augmented correlation-consistent polarized valance quadruple-zeta (aug-cc-pVQZ) basis set, the parametric 2-RDM method predicts a 27.5 kcal mol−1 barrier from ammonia oxide to hydroxylamine. We report reaction energies, barriers, geometries, and natural-orbital occupation numbers for the ammonia-oxide reaction and compare them to those from the oxywater reaction. We find that the parametric 2-RDM method agrees with dynamic correlation wavefunction methods when the multi-reference character of the system is small as in the ammonia-oxide isomerization computed here but that it captures additional multi-reference correlation, usually requiring a multi-reference method, when such correlation increases as in the oxywater isomerization.