Ding, F., Liang, W., Chapman, C. T., Isborn, C. M., & Li, X. (2011). On the gauge invariance of nonperturbative electronic dynamics using the time-dependent Hartree-Fock and time-dependent Kohn-Sham. Journal of Chemical Physics, 135, 164101. Abstract
Nonperturbative electronic dynamics using the time-dependent Hartree-Fock (TDHF) and time-dependent Kohn-Sham (TDKS) theories with the adiabatic approximation is a powerful tool in obtaining insights into the interaction between a many-electron system and an external electromagnetic field. In practical applications of TDHF/TDKS using a truncated basis set, the electronic dynamics and molecular properties become gauge-dependent. Numerical simulations are carried out in the length gauge and velocity gauge to verify the extent of gauge-dependence using incomplete basis sets. Electronic dynamics of two many-electron systems, a helium atom and a carbon monoxide molecule in high-intensity linearly polarized radiation fields are performed using the TDHF and TDKS with two selected adiabatic exchange-correlation (xc) functionals. The time evolution of the expectation values of the dipole moment and harmonic spectra are calculated in the two gauges, and the basis set dependence on the gauge-invariance of these properties is investigated.
Bing, Y., Selassie, D., Paradise, R. H., Isborn, C., Kramer, N., Sadilek, M., Kaminsky, W., et al. (2010). {Circular dichroism tensor of a triarylmethyl propeller in sodium chlorate crystals}. Journal of the American Chemical Society, 132, 7454–7465. Abstract
In 1919, Perucca reported anomalous optical rotatory dispersion from chiral NaClO(3) crystals that were colored by having been grown from a solution containing an equilibrium racemic mixture of a triarylmethane dye (Perucca, E. Nuovo Cimento 1919, 18, 112-154). Perucca's chiroptical observations are apparently consistent with a resolution of the propeller-shaped dye molecules by NaClO(3) crystals. This implies that Perucca achieved the first enantioselective adsorption of a racemic mixture on an inorganic crystal, providing evidence of the resolution of a triarylmethyl propeller compound lacking bulky ortho substituents. Following the earlier report, NaClO(3) crystals dyed with aniline blue are described herein. The rich linear optical properties of (001), (110), and (111) sections of these mixed crystals are described via their absorbance spectra in polarized light as well as images related to linear dichroism, linear birefringence, circular dichroism, and anomalous circular extinction. The linear dichroism fixes the transition electric dipole moments in the aromatic plane with respect to the growth faces of the NaClO(3) cubes. Likewise, circular dichroism measurements of four orientations of aniline blue in NaClO(3) fix a bisignate tensor with respect to the crystal growth faces. Electronic transition moments and circular dichroism tensors were computed ab initio for aniline blue. These calculations, in conjunction with the crystal-optical properties, establish a consistent mixed-crystal model. The nature of the circular extinction depends upon the crystallographic direction along which the crystals are examined. Along 100, the crystals evidence circular dichroism. Along 110, the crystals evidence mainly anomalous circular extinction. These two properties, while measured by the differential transmission of left and right circularly polarized light, are easily distinguished in their transformation properties with respect to reorientations of the sample plates. Circular dichroism is symmetric with respect to the wave vector, whereas anomalous circular extinction is antisymmetric. Analysis of Perucca's raw data reveals that he was observing a convolution of linear and circular optical properties. The relatively large circular dichroism should in principle establish the absolute configuration of the propeller-shaped molecules associated with d- or l-NaClO(3) crystals. However, this determination was not as straightforward as it appeared at the outset. In the solid state, unlike in solution, a strong chiroptical response is not in and of itself evidence of enantiomeric resolution. It is shown how it is possible to have a poor resolution-even an equal population of P and M propellers-within a given chiral NaClO(3) crystal and still have a large circular dichroism.
Fischer, S. A., Madrid, A. B., Isborn, C. M., & Prezhdo, O. V. (2010). {Multiple exciton generation in small Si clusters: A high-level, ab initio study}. Journal of Physical Chemistry Letters, 1, 232–237. Abstract
The electron hole excitonic nature of high energy states is investigated in neutral and charged Si clusters, motivated by the multiple exciton generation (MEG) process that is highly debated in photovoltaic literature, Silicon forms the basis for-much of the photovoltaic industry, and our high-level, first principles calculations show that at 2-3 times the lowest excitation energy, the majority of optically excited states in neutral Si, and Si 10 take on multiple exciton (ME) character. The transition from single excitons (SEs) to MEs is not as sharp in Si as in PbSe clusters, but it is much more pronounced than in CdSe. The closer similarity of Si to PbSe than CdSe is unexpected, since Si clusters are less symmetric than PbSe clusters. Charging suppresses MEG in Si clusters; however, the suppression is less pronounced than in PbSe. A strong ME signal is seen already at 5 X E(g) upon charging. The low ME thresholds and nearly complete switch from SEs to MEs create a good possibility for efficient MEG in neutral Si nanoclusters and reveal hope that reasonable quantum yields can still be obtained despite charging.
Liang, W., Isborn, C. M., Lindsay, A., Li, X., Smith, S. M., & Levis, R. J. (2010). {Time-dependent density functional theory calculations of ehrenfest dynamics of laser controlled dissociation of NO+: Pulse length and sequential multiple single-photon processes}. Journal of Physical Chemistry A, 114, 6201–6206. Abstract
Intense laser field controlled dissociation reactions of the nitric oxide cation (NO(+)) are studied by ab initio Ehrenfest dynamics with time-dependent density functional theory. Intense electric fields with five different pulse lengths are compared, combined with potential energy surface and density of state analysis, to reveal the effect of pulse length on the control mechanism. Controllable dissociative charge states are observed, and the correlation between the laser pulse length and the probability of sequential multiple single-photon processes is presented. This work introduces a concept of using laser pulse length to control the sequential multiple single-photon process.
Isborn, C. M., & Prezhdo, O. V. (2009). {Charging quenches multiple exciton generation in semiconductor nanocrystals: first-principles calculations on small PbSe clusters}. Journal of Physical Chemistry C, 113, 12617–12621. Abstract
We demonstrate using symmetry adapted cluster theory with configuration$\backslash$ninteraction \{(SAC-CI)\} that charging of small \{PbSe\} nanocrystals$\backslash$n\{(NCs)\} greatly modifies their electronic states and optical excitations.$\backslash$nConduction and valence band transitions that are not available in$\backslash$nneutral \{NCs\} dominate low energy electronic excitations and show$\backslash$nweak optical activity. At higher energies these transitions mix with$\backslash$nboth single excitons \{(SEs)\} and multiple excitons \{(MEs)\} associated$\backslash$nwith transitions across the band-gap. As a result, both \{SEs\} and$\backslash$n\{MEs\} are significantly blue-shifted, and \{ME\} generation is drastically$\backslash$nhampered. The overall contribution of \{MEs\} to the electronic excitations$\backslash$nof the charged \{NCs\} is small even at very high energies. The calculations$\backslash$nsupport the recent view that the observed strong dependence of the$\backslash$n\{ME\} yields on the experimental conditions is likely due to the effects$\backslash$nof \{NC\} charging.
Liang, W., Isborn, C. M., & Li, X. (2009). {Laser-controlled dissociation of C2H2(2+): Ehrenfest dynamics using time-dependent density functional theory.}. The journal of physical chemistry. A, 113, 3463–3469. Abstract
Intense laser field dissociations of the acetylene dication C(2)H(2)(2+) are studied by an ab initio Ehrenfest dynamics method with time-dependent density functional theory. Various field frequencies (9.5 to approximately 13.6 eV) and field directions are applied to a Boltzmann ensemble of C(2)H(2)(2+) molecules. With the laser field perpendicular to the molecular axis, four fragmentation channels are observed at high frequency with no dominant pathway. With the field parallel to the molecular axis, fragmentations occur at all frequencies and the amount of C-H bond breakage increases with laser frequency. Selective dissociation patterns are observed with low-frequency fields parallel to the molecular axis. A systematic analysis of excited-state potential energy surfaces is used to rationalize the simulation results.
The calculation of doubly excited states is one of the major problems plaguing the modern day excited state workhorse methodology of linear response time dependent Hartree-Fock (TDHF) and density function theory (TDDFT). We have previously shown that the use of a resonantly tuned field within real-time TDHF and TDDFT is able to simultaneously excite both the alpha and beta electrons to achieve the two-electron excited states of minimal basis H(2) and HeH(+) [C. M. Isborn and X. Li, J. Chem. Phys. 129, 204107 (2008)]. We now extend this method to many electron systems with the use of our Car-Parrinello density matrix search (CP-DMS) with a first-principles fictitious mass method for wave function optimization [X. Li, C. L. Moss, W. Liang, and Y. Feng, J. Chem. Phys. 130, 234115 (2009)]. Real-time TDHF/TDDFT is used during the application of the laser field perturbation, driving the electron density toward the doubly excited state. The CP-DMS method then converges the density to the nearest stationary state. We present these stationary state doubly excited state energies and properties at the HF and DFT levels for H(2), HeH(+), lithium hydride, ethylene, and butadiene.
Tretiak, S., Isborn, C. M., Niklasson, A. M. N., & Challacombe, M. (2009). {Representation independent algorithms for molecular response calculations in time-dependent self-consistent field theories}. Journal of Chemical Physics, 130. Abstract
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.
Isborn, C. M., & Li, X. (2009). {Singlet− Triplet Transitions in Real-Time Time-Dependent Hartree− Fock/Density Functional Theory}. Journal of Chemical Theory and Computation, 5, 2415–2419. Website Abstract
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
Badaeva, E., Isborn, C. M., Feng, Y., Ochsenbein, S. T., Gamelin, D. R., & Li, X. (2009). {Theoretical Characterization of Electronic Transitions in Co 2+ - and Mn 2+ -Doped ZnO Nanocrystals}. Journal of Physical Chemistry C, 113, 8710–8717. Abstract
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.
Takimoto, Y., Isborn, C. M., Eichinger, B. E., Rehr, J. J., & Robinson, B. H. (2008). {Frequency and solvent dependence of nonlinear optical properties of molecules}. Journal of Physical Chemistry C, 112, 8016–8021. Abstract
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.
Isborn, C. M., Kilina, S. V., Li, X., & Prezhdo, O. V. (2008). {Generation of multiple excitons in PbSe and CdSe quantum dots by direct photoexcitation: First-principles calculations on small PbSe and CdSe clusters}. Journal of Physical Chemistry C, 112, 18291–18294. Abstract
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.
Hrovat, D., Isborn, C. M., Kahr, B., & Borden, W. T. (2008). Internal Dynamics and Optical Rotations Predicted for O h - and O-Symmetric Cubanes. Organic Letters, 85–87.
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.
Claborn, K., Isborn, C., Kaminsky, W., & Kahr, B. (2008). {Optical rotation of achiral compounds}. Angewandte Chemie - International Edition, 47, 5706–5717. Abstract
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.
Isborn, C. M., a. Leclercq,, Vila, F. D., Dalton, L. R., Brédas, J. L., Eichinger, B. E., & Robinson, B. H. (2007). {Comparison of static first hyperpolarizabilities calculated with various quantum mechanical methods}. Journal of Physical Chemistry A, 111, 1319–1327. Abstract
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.
Wustholz, K. L., Bott, E. D., Isborn, C. M., Li, X., Kahr, B., & Reid, P. J. (2007). {Dispersive kinetics from single molecules oriented in single crystals of potassium acid phthalate}. Journal of Physical Chemistry C, 111, 9146–9156.
Isborn, C., Claborn, K., & Kahr, B. (2007). {The optical rotatory power of water}. Journal of Physical Chemistry A, 111, 7800–7804. Abstract
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.