Electron–vibration coupling in time-dependent density-functional theory: Application to benzene

Valence ππ* Excitations in Benzene Studied by Multiconfiguration Pair-Density Functional Theory

We explore the valence singlet and triplet ππ* excitations of benzene with complete active pace self-consistent field (CASSCF) theory, complete active space perturbation theory (CASPT2), and multiconfiguration pair-density functional theory (MC-PDFT) for four different choices of active space. We propose a new way to quantify the covalent and ionic character of the electronic states in terms of the components of the total electronic energy. We also explore the effect of scaling the exchange and correlation components of the on-top density functional used in MC-PDFT; we observe that increasing the exchange contribution improves the MC-PDFT excitation energies for benzene.

Substituent and Solvent Effects on the Absorption Spectra of Cation-π Complexes of Benzene and Borazine: A Theoretical Study

Time-dependent density functional theory (TDDFT) has been used to predict the absorption spectra of cation-π complexes of benzene and borazine. Both polarized continuum model (PCM) and discrete solvation model (DSM) and a combined effect of PCM and DSM on the absorption spectra have been elucidated. With decrease in size of the cation, the π → π* transitions of benzene and borazine are found to undergo blue and red shift, respectively. A number of different substituents (both electron-withdrawing and electron-donating) and a range of solvents (nonpolar to polar) have been considered to understand the effect of substituent and solvents on the absorption spectra of the cation-π complexes of benzene and borazine. Red shift in the absorption spectra of benzene cation-π complexes are observed with both electron-donating groups (EDGs) and electron-withdrawing groups (EWGs). The same trend has not been observed in the case of substituted borazine cation-π complexes. The wavelength of the electronic transitions corresponding to cation-π complexes correlates well with the Hammet constants (σ_p and σ_m). This correlation indicates that the shifting of spectral lines of the cation-π complexes on substitution is due to both resonance and inductive effect. On incorporation of solvent phases, significant red or blue shifting in the absorption spectra of the complexes has been observed. Kamlet-Taft multiparametric equation has been used to explain the effect of solvent on the absorption spectra of complexes. Polarity and polarizability are observed to play an important role in the solvatochromism of the cation-π complexes.

Time dependent density functional theory with DMol3

Time dependent density function theory (TDDFT) has been implemented in the program DMol(3), a local atomic orbital implementation of DFT. Scaling and computation times for typical TDDFT calculations are comparable to DFT-SCF calculations. The implementation is fully parallel. Three applications are presented to show what quantitative and qualitative effects can be predicted by the present implementation. These include atomic multiplets of Ti(4+), UV-vis spectra of aromatic organic molecules, and a mapping versus the reaction coordinate of the excited state potential energy surfaces of the nitroprusside ion (Fe(CN)(5)NO)(-2).

The prediction of the circular dichroism of the benzene chromophore: TDDFT calculations and sector rules

The CD spectra of the series PhCH(Me)R, with R = Et (1), nPr (2), iPr (3), and tBu (4), are reported (1-3 for the first time) at room temperature in the 185-280 nm range and at 183 K. These purely hydrocarbon compounds represent the simplest chiral systems containing the phenyl chromophore and exhibit Cotton effects exclusively allied with the benzene transitions. The bands in 1La and 1Lb regions were checked against the available sector rules, with discordant outcomes. Time-dependent density-functional theory calculations, with various functionals and basis sets tested, correctly reproduced the prominent CD bands observed for 1-4.

Time-Dependent Density-Functional Studies of the D2 Coulomb Explosion

Real-time first principle simulations are presented of the D(2) Coulomb explosion dynamics detonated by exposure to very intense few-cycle laser pulse. Three approximate functionals within the time-dependent density functional theory (TDDFT) functionals are examined for describing the electron dynamics, including time-dependent Hartree-Fock theory. Nuclei are treated classically with quantum corrections. The calculated results are sensitive to the underlying electronic structure theory, showing too narrow kinetic energy distribution peaked at too high kinetic energy when compared with recent experimental results (Phys. Rev. Lett. 2003, 91, 093002). Experiment also shows a low energy peak which is not seen in the present calculation. We conclude that while Ehrenfest-adiabatic-TDDFT can qualitatively account for the dynamics, it requires further development, probably beyond the adiabatic approximation, to be quantitative.

Ground- and excited-state electronic structure of an iron-containing molecular spin photoswitch

The electronic structure of the cation of [Fe(ptz)(6)](BF(4))(2), a prototype of a class of complexes that display light-induced excited-state spin trapping (LIESST), has been investigated by time-independent and time-dependent density-functional theories. The density of states of the singlet ground state reveals that the highest occupied orbitals are metal centered and give rise to a low spin configuration Fe(2+)(3d(xy) ( upward arrow downward arrow)3d(xz) ( upward arrow downward arrow)3d(yz) ( upward arrow downward arrow)) in agreement with experiment. Upon excitation with light in the 2.3-3.3 eV range, metal-centered spin-allowed but parity-forbidden ligand field (LF) antibonding states are populated which, in conjunction with electron-phonon coupling, explain the experimental absorption intensities. The computed excitation energies are in excellent agreement with experiment. Contrary to simpler models we show that the LF absorption bands, which are important for LIESST, do not originate in transitions from the ground to a single excited state but from transitions to manifolds of nearly degenerate excited singlets. Consistent with crystallography, population of the LF states promotes a drastic dilation of the ligand cage surrounding the iron.

Exploratory study of the electron-density relocalization process in benzene through a time-dependent topological analysis

A time-dependent topological analysis of the electron density in benzene provides quantitative information about charge oscillation processes, and particularly about the two highest pi orbitals contributions to carbon topological basins. In this exploratory study coupling one molecular-dynamic trajectory to a topological analysis, Fourier transform of the topological time data autocorrelation functions indicates frequencies of oscillations, and shows that carbon atoms, though identical in average, would be more or less highest occupied molecular-orbital reactive with a cyclic behavior.

Dynamic Evolution of Kohn-Sham Electron Density in the Real-Time Domain with Finite Basis Expansion

We present a novel method for time-dependent density functional theory calculations on dynamic linear response and electron density evolution in the real-time domain with the finite basis expansion approach of conventional quantum chemistry. To demonstrate the validity and efficiency of this method, dynamic polarizabilities of a water chain and diphenylene molecules are computed by employing the Chebyshev interpolation algorithm, which was developed by Baer and co-workers. The calculated dynamic polarizabilities show good agreement with those obtained from conventional linear response calculations. The density evolution in the real-time domain with application of a long-duration electric field gives electronic conduction in molecules, where a dynamic process of charge transfer is observed with the snapshots of response density in real time. Charge transfer oscillating with the frequency of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) gap is shown in a diphenylene molecule while there is little change in time for a water chain.

Real-time linear response for time-dependent density-functional theory

We present a linear-response approach for time-dependent density-functional theories using time-adiabatic functionals. The resulting theory can be performed both in the time and in the frequency domain. The derivation considers an impulsive perturbation after which the Kohn-Sham orbitals develop in time autonomously. The equation describing the evolution is not strictly linear in the wave function representation. Only after going into a symplectic real-spinor representation does the linearity make itself explicit. For performing the numerical integration of the resulting equations, yielding the linear response in time, we develop a modified Chebyshev expansion approach. The frequency domain is easily accessible as well by changing the coefficients of the Chebyshev polynomial, yielding the expansion of a formal symplectic Green's operator.