Andrew M. Sand

Synthesis and Photophysics of Benzotexaphyrin : A Near-Infrared Emitter and Photosensitizer

Texaphyrins are pentaazadentate macrocycles with interesting photophysical properties and potential applications as nonlinear optical (NLO) materials, photosensitizers, magnetic resonance imaging (MRI) contrasting reagents, and radiation sensitizers, etc. To further red-shift the Q-like band of the texaphyrins, a benzotexaphyrin with an extensively delocalized pi-electron system was synthesized for the first time. Its photophysical characteristics were systematically investigated. Due to the extended pi-conjugation, the Q(0,0) band of benzotexaphyrin bathochromically shifts to 810 nm, and it emits at 825 nm with a singlet excited-state lifetime of 895 ps. Its triplet excited-state energy is estimated to be 119 kJ/mol. The triplet excited-state lifetime is approximately 2.2 micros, and the quantum yield of the triplet excited-state formation is 0.78. It also exhibits a triplet-triplet transient absorption in the region 505-590 nm. In addition, benzotexaphyrin exhibits high efficiency in generating singlet oxygen in methanol (Phi(Delta) = 0.65). Therefore, benzotexaphyrin could potentially be a NIR photosensitizer and emitter for photodynamic therapy and bioimaging applications.

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.

Correlated-Participating-Orbitals Pair-Density Functional Method and Application to Multiplet Energy Splittings of Main-Group Divalent Radicals.

Predicting the singlet-triplet splittings of divalent radicals is a challenging task for electronic structure theory. In the present work, we investigate the performance of multiconfiguration pair-density functional theory (MC-PDFT) for computing the singlet-triplet splitting for small main-group divalent radicals for which accurate experimental data are available. In order to define theoretical model chemistries that can be assessed consistently, we define three correlated participating orbitals (CPO) schemes (nominal, moderate, and extended, abbreviated as nom, mod, and ext) to define the constitution of complete active spaces, and we test them systematically. Broken-symmetry Kohn-Sham DFT calculations have also been carried out for comparison. We found that the extended CPO-PDFT scheme with translated on-top pair-density functionals have smaller mean unsigned errors than weighted-average broken-symmetry Kohn-Sham DFT with the corresponding exchange-correlation functional. The accuracy of the translated Perdew-Burke-Ernzerhof (tPBE) on-top pair-density functionals with ext-CPO active space is even better than some of the more accurately parametrized exchange-correlation density functionals that we tested; this is very encouraging for MC-PDFT theory.

Efficient algorithm for multiconfiguration pair-density functional theory with application to the heterolytic dissociation energy of ferrocene

The recently developed multiconfiguration pair-density functional theory (MC-PDFT) combines multiconfiguration wave function theory with a density functional that depends on the on-top pair density of an electronic system. In an MC-PDFT calculation, there are two steps: a conventional multiconfiguration self-consistent-field (MCSCF) calculation and a post-MCSCF evaluation of the energy with an on-top density functional. In this work, we present the details of the MC-PDFT algorithm that avoids steeply scaling steps that are present in other post-self-consistent-field multireference calculations of dynamic correlation energy. We demonstrate the favorable scaling by considering systems of H2 molecules with active spaces of several different sizes. We then apply the MC-PDFT method to calculate the heterolytic dissociation enthalpy of ferrocene. We find that MC-PDFT yields results that are at least as accurate as complete active space second-order perturbation theory and are more stable with respect to basis set, but at a fraction of the cost in both time and memory.

Effect of molecular-orbital rotations on ground-state energies in the parametric two-electron reduced density matrix method

Different sets of molecular orbitals and the rotations connecting them are of great significance in molecular electronic structure. Most electron correlation methods depend on a reference wave function that separates the orbitals into occupied and unoccupied spaces. Energies and properties from these methods depend upon rotations between the spaces. Some electronic structure methods, such as modified coupled electron pair approximations and the recently developed parametric two-electron reduced density matrix (2-RDM) methods [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], also depend upon rotations between occupied orbitals and rotations between unoccupied orbitals. In this paper, we explore the sensitivity of the ground-state energies from the parametric 2-RDM method to rotations within the occupied space and within the unoccupied space. We discuss the theoretical origin of the rotational dependence and provide computational examples at both equilibrium and non-equilibrium geometries. We also study the effect of these rotations on the size extensivity of the parametric 2-RDM method. Computations show that the orbital rotations have a small effect upon the parametric 2-RDM energies in comparison to the energy differences observed between methodologies such as coupled cluster and parametric 2-RDM. Furthermore, while the 2-RDM method is rigorously size extensive in a local molecular orbital basis set, calculations reveal negligible deviations in nonlocal molecular orbital basis sets such as those from canonical Hartree-Fock calculations.

Enhanced computational efficiency in the direct determination of the two-electron reduced density matrix from the anti-Hermitian contracted Schrödinger equation with application to ground and excited states of conjugated π-systems

Determination of the two-electron reduced density matrix (2-RDM) from the solution of the anti-Hermitian contracted Schrödinger equation (ACSE) yields accurate energies and properties for both ground and excited states. Here, we develop a more efficient method to solving the ACSE that uses second-order information to select a more optimal step towards the solution. Calculations on the ground and excited states of water, hydrogen fluoride, and conjugated π systems show that the improved ACSE algorithm is 10-20 times faster than the previous ACSE algorithm. The ACSE can treat both single- and multi-reference electron correlation with the initial 2-RDM from a complete-active-space self-consistent-field (CASSCF) calculation. Using the improved algorithm, we explore the relationship between truncation of the active space in the CASSCF calculation and the accuracy of the energy and 2-RDM from the ACSE calculation. The accuracy of the ACSE, we find, is less sensitive to the size of the active space than the accuracy of other wavefunction methods, which is useful when large active space calculations are computationally infeasible.

Modulating the electronic structure of chromophores by chemical substituents for efficient energy transfer: Application to fluorone

Strong electron correlation within a quasi-spin model of chromophores was recently shown to enhance exciton energy transfer significantly. Here we investigate how the modulation of the electronic structure of the chromophores by chemical substitution can enhance energy-transfer efficiency. Unlike previous work that does not consider the direct effect of the electronic structure on exciton dynamics, we add chemical substituents to the fluorone dimer to study the effect of electron-donating and electron-withdrawing substituents on exciton energy transfer. The exciton dynamics are studied from the solution of a quantum Liouville equation for an open system whose model Hamiltonian is derived from excited-state electronic structure calculations. Both van der Waals energies and coupling energies, arising from the Hellmann-Feynman force generated upon transferring the dimers from infinity to a finite separation, are built into the model Hamiltonian. Though these two effects are implicitly treated in dipole-based models, their explicit and separate treatment as discussed here is critical to forging the correct connection with the electronic structure calculations. We find that the addition of electron-donating substituents to the fluorone system results in an increase in exciton-transfer rates by factors ranging from 1.3-1.9. The computed oscillator strength is consistent with the recent experimental results on a larger heterodimer system containing fluorone. The oscillator strength increases with the addition of electron-donating substituents. Our results indicate that the study of chromophore networks via electronic structure will help in the future design of efficient synthetic light-harvesting systems.

Analytic Gradients for Complete Active Space Pair-Density Functional Theory

Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters. We find that MC-PDFT locates equilibrium geometries for several small- to medium-sized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost.

State-interaction pair-density functional theory

The accurate description of ground- and excited-state potential energy surfaces poses a challenge for many electronic structure methods, especially in regions where strong electronic state interaction occurs. Here we introduce a new methodology, state-interaction pair-density functional theory (SI-PDFT), to target molecular systems exhibiting strong interaction of electronic states. SI-PDFT is an extension of multiconfiguration pair-density functional theory in which a set of N electronic states is generated through the diagonalization of an N × N effective Hamiltonian. We demonstrate the accuracy of the method by performing calculations on the ionic-neutral avoided crossing in lithium fluoride and the 1ππ-1πσ* avoided crossing in the H-O bond photodissociation in phenol. We show that SI-PDFT can be a useful tool in the study of photochemistry and nonadiabatic dynamics.