Four different numerical algorithms suitable for a linear scaling implementation of time-dependent Hartree-Fock and Kohn-Sham self-consistent field theories are examined. We compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures to solve the random-phase approximation (RPA) (non-Hermitian) and Tamm-Dancoff approximation (TDA) (Hermitian) eigenvalue equations in the molecular orbital-free framework. Semiempirical Hamiltonian models are used to numerically benchmark algorithms for the computation of excited states of realistic molecular systems (conjugated polymers and carbon nanotubes). Convergence behavior and stability are tested with respect to a numerical noise imposed to simulate linear scaling conditions. The results single out the most suitable procedures for linear scaling large-scale time-dependent perturbation theory calculations of electronic excitations.
Real-time time-dependent Hartree-Fock (TDHF)/density functional theory (TDDFT) has been gaining in popularity because of its ability to treat phenomena beyond the linear response and because it has the potential to be more computationally powerful than frequency domain TDHF/TDDFT. Within real-time TDHF/TDDFT, we present a method that gives the excited state triplet energies starting from a singlet ground state. Using a spin-dependent field, we break the spin-symmetry of the R and ? density matrices, which incorporates a triplet contribution into the superposition state. The R electron density follows the applied field, and the ? electron density responds to the perturbation from the changing R electron density. We examine the individual R/? responses during the electron density propagation. Singlet-triplet transitions appear as ‘dark’ states: they are present in the R/? responses but are absent from the total electron density response
Linear response time-dependent hybrid density functional theory has been applied for the first time to describe optical transitions characteristic of Co2+- and Mn2+-doped ZnO quantum dots (QDs) with sizes up to 300 atoms (∼1.8 nm diam) and to investigate QD size effects on the absorption spectra. Particular attention is given to charge-transfer (CT or “photoionization”) excited states. For both dopants, CT transitions are calculated to appear at sub-band-gap energies and extend into the ZnO excitonic region. CT transitions involving excitation of dopant d electrons to the ZnO conduction band occur lowest in energy, and additional CT transitions corresponding to promotion of ZnO valence band electrons to the dopant d orbitals are found at higher energies, consistent with experimental results. The CT energies are found to depend on the QD diameter. Analysis of excited-state electron and hole density distributions shows that, for both CT types, the electron and hole are localized to some extent around the impurity ion, which results in “heavier” photogenerated carriers than predicted from simple effective mass considerations. In addition to CT transitions, the Co2+-doped ZnO QDs also exhibit characteristic d-d excitations whose experimental energies are reproduced well and do not depend on the size of the QD.
Real-time, time-dependent density functional theory (RT-TDDFT) is used for the evaluation of the frequency dependence of the polarizability and hyperpolarizability of molecules intended for application in electro-optic devices. These first-principles computational methods are powerful but costly. Significantly easier calculations based on a simplified version of second-order time-dependent perturbation theory, the ``two-state model'' (TSM), are here used to provide another estimate of the frequency dependence. Furthermore, the TSM calculations can be done in the presence of a dielectric reaction field (the polarizable continuum model method) to provide estimates of the solvent dependent properties in addition to the frequency-dependent properties. Here we use RT-TDDFT to assess the accuracy of the frequency dependence of the TS, and a ground-state finite field calculation to assess the effect of additional states on the static hyperpolarizability. Both frequency and dielectric responses are important for evaluation of the suitability of molecules in nonlinear optical applications.
We demonstrate for the first time using a combination of the Hartree?Fock approximation and the symmetry adapted cluster theory with configuration interaction (SAC-CI) that multiple excitons (ME) in PbSe and CdSe quantum dots (QD) can be generated directly upon photoexcitation. At energies 2.5?3 times the lowest excitation, almost all optically excited states in Pb4Se4 become MEs, while both single excitons and MEs are seen in Cd6Se6. We analyze the high-level SAC-CI results of the small clusters based on the band structure and then extend our band structure analysis to Pb68Se68, Pb180Se180, Cd33Se33, and Cd111Se111. Our results explain the ultrafast generation of MEs without the need for a phonon relaxation bottleneck and clarify why PbSe is particularly suitable for generation of MEs. Efficient exciton multiplication can be used to considerably increase the efficiency of QD-based solar cells.
Multielectron excited states have become a hot topic in many cutting-edge research fields, such as the photophysics of polyenes and in the possibility of multiexciton generation in quantum dots for the purpose of increasing solar cell efficiency. However, obtaining multielectron excited states has been a major obstacle as it is often done with multiconfigurational methods, which involve formidable computational cost for large systems. Although they are computationally much cheaper than multiconfigurational wave function based methods, linear response adiabatic time-dependent Hartree-Fock (TDHF) and density functional theory (TDDFT) are generally considered incapable of obtaining multielectron excited states. We have developed a real-time TDHF and adiabatic TDDFT approach that is beyond the perturbative regime. We show that TDHF/TDDFT is able to simultaneously excite two electrons from the ground state to the doubly excited state and that the real-time TDHF/TDDFT implicitly includes double excitation within a superposition state. We also present a multireference linear response theory to show that the real-time electron density response corresponds to a superposition of perturbative linear responses of the S(0) and S(2) states. As a result, the energy of the two-electron doubly excited state can be obtained with several different approaches. This is done within the adiabatic approximation of TDDFT, a realm in which the doubly excited state has been deemed missing. We report results on simple two-electron systems, including the energies and dipole moments for the two-electron excited states of H(2) and HeH(+). These results are compared to those obtained with the full configuration interaction method.
Oriented achiral molecules and crystals with D(2d) symmetry or one of its non-enantiomorphous subgroups, S(4), C(2v), or C(s), can rotate the plane of transmitted polarized light incident in a general direction. This well-established fact of crystal optics is contrary to the teaching of optical activity to students of organic chemistry. This Minireview gives an overview of the measurement and calculation of the chiroptical properties of some achiral compounds and crystals. Methane derivatives with four identical ligands related by reflection symmetry are quintessential optically inactive compounds according to the logic of van't Hoff. Analysis of the optical activity of simple achiral compounds such as H(2)O and NH(3) provides general aspects of chiroptics that are not readily broached when considering chiral compounds exclusively. We show here, through the use of group theoretical arguments, the transformation properties of tensors, and diagrams, why some achiral, acentric compounds are optically active while others are not.
The prediction of nonlinear electro-optic (EO) behavior of molecules with quantum methods is the first step in the development of organic-based electro-optic devices. Typical EO molecules may require calculations with several hundred electrons, which prevents all but the fastest methods (semiempirical and density functional theory (DFT)) from being used for EO estimation. To test the reliability of these methods, we compare dipole moments, polarizabilities, and first-order hyperpolarizabilities for a wide range of structures of experimental interest with Hartree-Fock (HF), intermediate neglect of differential overlap (INDO), and DFT methods. The relative merits of molecules are consistently predictable with every method.
Ab initio molecular orbital calculations of the optical rotatory response of a single oriented water molecule are described. The unique tensor element g(xy) was computed to be -0.047 bohr(3) with CCSD/6-311+G(d,p). A value of -0.033 was obtained with the minimal valence basis that was better suited to parsing the rotatory response among a limited number of excited states. Transition moments were calculated ab initio and qualitatively derived from the wave functions. Rotations were reckoned from the relative dispositions of the transition moments with respect to the wavevectors. In this way, it was possible to intuitively reckon the form of the optical rotation tensor consistent with that from higher levels of theory and to establish which excitations make the most significant contributions.
An ab initio direct Ehrenfest dynamics method with time-dependent density functional theory is introduced and applied to collisions of 5 eV oxygen atoms and ions with graphite clusters. Collisions at three different sites are simulated. Kinetic energy transfer from the atomic oxygen to graphite local vibrations is observed and electron-nuclear coupling resulting in electronic excitation within the graphite surface as well as alteration of the atomic charge is first reported in this paper. The three oxygen species studied, O(3P), O-(2P), and O+(4S), deposit different amounts of energy to the surface, with the highest degree of damage to the pi conjugation of the cluster produced by the atomic oxygen cation. Memory of the initial charge state is not lost as the atom approaches, in contrast to the usual assumption.
We investigated the nature of the ground state and static response properties (mu, alpha, and beta) for a promising class of twisted pi-electron system nonlinear optical chromophores at the HF, B3LYP, MP2, and CASSCF levels. We report results for a substituted twisted ethylene and a larger tictoid analogue. Previous work has reported only a zwitterionic character for such tictoid species, however, (14,13) CASSCF calculations predict a ground-state diradical. At the HF, B3LYP, MP2, and (14,13) CASSCF levels, the values of beta are orders of magnitude smaller than those predicted by semiempirical methods.
The influence of rotational and geometrical isomerism on the nonlinear optical (NLO) properties, specifically the first-order hyperpolarizability beta, of chromophores of current interest has been investigated with density functional theory (DFT). In the first of this two-part study, the rotational isomerism of a linear chromophore was explored. Calculation of the torsion potentials about two of the rotatable and conformation-changing single bonds in a chromophore demonstrated the near equality of the molecular energies at 0 degrees and 180 degrees rotational angles. To explore the consequences of this near conformational energy degeneracy to NLO behavior, the eight low energy rotational isomers of FTC [Robinson, B. H.; et al. Chem. Phys. 1999, 245, 35] were investigated. This study provides the first-reported DFT-based calculation of the statistical mechanical average of beta over the conformational space of a molecule having substantial nonlinear optical behavior. The influence of the solvent reaction field on rotameric populations and on the beta tensor is reported. In the second part, two molecules having two donors and two acceptors bonded respectively in ortho and meta positions on a central benzene ring are shown to have substantially different beta tensors. These two so-called molecular Xs have different highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) distributions, and consistent with expectations, it is found that the larger beta(zzz) is associated with a large spatial asymmetry between the HOMOs and LUMOs. Large hyperpolarizability correlates with the HOMO concentrated on the donor groups and the LUMO on the acceptor groups.
The optical rotatory power of achiral crystals of achiral pentaerythritol molecules was measured. The maximum rotations were found to be +/-6 degrees /mm. The quantum mechanically computed rotation of pentaerythritol molecules using linear response theory was 6 times larger although the experimental and theoretical tensors were similarly oriented to within 5 degrees .
High-level electronic structure calculations have been used to study the factors contributing to the barriers to degenerate hydrogen-atom transfer (HAT) reactions. Understanding of these reactions is a prerequisite to the development of any more general theory of HAT reactions, and yet, the existing models for such reactions perform quite poorly when applied to even simple self-exchanges. The reasons behind these failures are elucidated in the present work. They include a near cancellation of bond-strength effects between reactant and transition state, as well as a strong dependence of the geometry of the transition state on the nature of the heavy atoms.
Aromatic Möbius [4n]annulenes with 4n pi electrons, originally conceived by Heilbronner, are characterized computationally. These (CH)(12), (CH)(16), and (CH)(20) minima have nearly equal C-C bond lengths, small twist angles around the rings, and magnetic properties (NICS, nucleus-independent chemical shifts–see above at various positions in annulene–and magnetic susceptibility exaltations) indicating significantly diatropic ring currents. The Möbius forms are not the most stable isomers but may contribute significantly to the chemistry of these annulenes. [structure: see text]