Dynamic second order properties of H2O2

Electric static and dynamic polarizability and optical rotatory power have been calculated for H₂O₂ utilizing coupled Hartree–Fock time-dependent perturbation theory.     

Generalization of the Forster resonance energy transfer theory for quantum mechanical modulation of the donor-acceptor coupling

The Forster resonance energy transfer theory is generalized for inelastic situations with quantum mechanical modulation of the donor-acceptor coupling. Under the assumption that the modulations are independent of the electronic excitation of the donor and the acceptor, a general rate expression is derived, which involves two dimensional frequency-domain convolution of the donor emission line shape, the acceptor absorption line shape, and the spectral density of the modulation of the donor-acceptor coupling. For two models of modulation, detailed rate expressions are derived. The first model is the fluctuation of the donor-acceptor distance, approximated as a quantum harmonic oscillator coupled to a bath of other quantum harmonic oscillators. The distance fluctuation results in additional terms in the rate, which in the small fluctuation limit depend on the inverse eighth power of the donor-acceptor distance. The second model is the fluctuation of the torsional angle between the two transition dipoles, which is modeled as a quantum harmonic oscillator coupled to a bath of quantum harmonic oscillators and causes sinusoidal modulation of the donor-acceptor coupling. The rate expression has new elastic and inelastic terms, depending sensitively on the value of the minimum energy torsional angle. Experimental implications of the present theory and some of the open theoretical issues are discussed.     

Induced optical activity in non-associated systems

Circular dichroism bands can appear at absorption frequencies of achiral molecules when chiral species (which do not associate with the achiral molecules) are added to the solution. The induced activity in the achiral species is rationalised as the result of van der Waals' coupling to the chiral species. An expression is derived for the induced rotatory strength when all molecules in the solution are assumed to be freely rotating, so that there is no orientational correlation of their relative motions. The application of the theory of the induced activity in carbonyl compounds is qualitatively discussed.     

Time-dependent density functional theory for calculating origin-independent optical rotation and rotatory strength tensors

An approach to calculate origin-independent electronic chiroptical property tensors using time-dependent density functional theory (TDDFT) and gauge-including atomic orbital (GIAO) basis sets is evaluated. Computations of origin-dependent optical rotation tensors and of rotatory strengths needed to simulate circular dichroism spectra are presented. The optical rotation tensor computations employ solutions of coupled perturbed Kohn-Sham equations for a dynamic electric field and a static magnetic field. Because the magnetic field is time independent, the GIAO treatment is somewhat simplified compared to a previously reported method, at some added computational cost if hybrid functionals are employed. GIAO rotatory strengths are also calculated, using transition density matrices from a standard TDDFT excitation energy module. A new implementation in the NWChem quantum chemistry package is employed for representative computations of origin-invariant chiroptical response tensors for methyloxirane, norbornenone, and the ketosteroid androstadienone. For the steroid molecule the vibrational structure of the CD spectrum is modeled explicitly by using calculated Franck-Condon factors. The agreement with experiment is favorable.     

Size evolution study of "molecular" and "atom-in-cluster" polarizabilities of medium-size gold clusters

A study on static polarizabilities for a family of gold clusters (Au(n), n = 6, 12, 20, 34, 54) is presented. For each cluster, a density functional theory perturbation theory calculation was performed to compute the cluster polarizability and the polarizability of each atom in the cluster using Bader's "quantum theory of atoms in molecules" formalism. The cluster polarizability tensor, α(cluster), is expressed as a sum of the atom-in-molecule tensors, α(cluster)=∑(Ω)α(Ω). A strong quadratic correlation (R(2) = 0.98) in the isotropic polarizability of atoms in the cluster and their distance to the cluster center of mass was observed. The cluster polarizabilities are in agreement with previous calculations.     

Theory of the absorption and circular dichroism spectra of helical molecular aggregates

A theory of the electronic circular dichroism (CD) and optical rotatory dispersion (ORD) of infinite aggregates exhibiting cylindrical symmetry is presented in which, to the authors' knowledge, for the first time vibrational structure is included explicitly. It is shown that, with the coherent exciton scattering approximation in the Green function approach, the detailed vibrational structure of the aggregate absorption. CD and ORD bands can be calculated from a knowledge of the electronic coupling and the monomer absorption line shape alone. Detailed model calculations for a single helix are made and the results are used to expose the origin of different spectral features. A good reproduction of experimental J-aggregate spectra is obtained, using the same electronic interaction to fit both absorption and CD spectral line shapes. The theory allows some prediction of aggregate geometry to be made, but it is shown that an unambiguous geometrical assignment can only be made where experimental spectra for light of different propagation directions with respect to the cylinder axis are available.     

Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions

The complex linear response function, which can be employed for calculations of second-order molecular properties in regions of strong absorption, is here extended to encompass the mixed electric-dipole-magnetic-dipole polarizability. The mixed electric-dipole-magnetic-dipole polarizability determines the optical rotation and, when absorption is taken into account, the full anomalous optical rotatory dispersion (ORD) spectra of chiral molecules can be calculated using first-principle quantum-chemical methods. Gauge-origin independence of the results is ensured through the use of London atomic orbitals. To illustrate the importance of taking the absorption process properly into account, we here apply this methodology to the study of the anomalous ORD of hydrogen peroxide, 3R-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)-ferrocenophan-2-on, and the D(2) isomer of the C(84) fullerene.     

共轭烯烃的共轭极化势

Based on the conjugated polarization theory,it is expressed as the conjugated polarizability potential （CPP）that the discrepancy between the average electrostatic energy of dipolar state and the electrostatic energy of non-polar state in the conjugated polarizability procedure for the conjugated alkenes. The correlation between CPP and the energy of ultraviolet absorption maximum,and the correlation between the energy of frontier molecular orbital obtained by ab initio calculation of quantum chemistry and the energy of ultraviolet absorption maximum have been carried out for the conjugated alkenes. Both correlation equations show a similar estimated precision. Further, the contribution of alkyl polarizability effect to the stability of dipolar state for the alkyl substituted alkenes with the effective polarizability effect index（PEI（ef））was quantified. Relating the above two parameters CPP and PEI（ef）to the energy of ultraviolet absorption maximum of the substituted alkenes in a two-parameter expression with a good prediction ability was obtained:v=1.1746+5.0187CPP-0.43204PEI （ef）,R=0.9995,s=0.0403,F=10853.28,n=23. The investigated results also indicate that it is less effective to reduce the energy of ultraviolet absorption maximum by means of increasing the alkyl substituent groups than lengthening the conjugated backbone chain in the conjugated alkenes.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Polarizability of small carbon cluster anions from first principles

We examine the applicability of density functional theory (DFT) to the polarizability of Cn- (n = 3-9) cluster anions. This was achieved by comparing DFT calculations using two different exchange-correlation functionals (the non-empirical local density approximation, LDA, and the semiempirical hybrid functional B97-1) to quantum chemical calculations using the coupled cluster method in the CCSD(T) "gold standard" approximation. We find that, unless the extra electron is not bound at all by DFT, both LDA and B97-1 agree with the CCSD(T) calculation to within 5-10%, allowing for a meaningful qualitative and semiquantitative analysis. Furthermore, the polarizability is found to increase monotonically with chain size, consistent with the trend inferred from electron detachment experiments.     

Ab initio calculation of optical rotation in (P)-(+)-[4]triangulane

Optical rotation, the angle through which plane-polarized light rotates when passed through an enantiomerically pure medium, plays a vital role in the determination of the absolute configurations of chiral molecules such as natural products. We describe new quantum mechanical methodology designed to assist in this endeavor by providing high-accuracy computational optical rotatory dispersion data for matching to experimental results. Comparison between theory and experiment for the rigid, helical molecule trispiro[2.0.0.2.1.1]nonane [also known as (P)-(+)-[4]triangulane], recently synthesized with enantiomeric purity, shows that the coupled cluster quantum chemical model provides superb agreement for optical rotation across a wide range of wavelengths (589-365 nm), with errors averaging only 1%.     

Time-dependent quantum theory II. Absorption of light by dimers: Quantum theory and classical analogy

The quantum theory of light absorption by a pair of neighboring absorbers is developed in the point dipole approximation for the circumstance where excited states decay only by radiative damping. Comparison with classical local field theories, in which the monomers are represented by constant, frequency-dependent complex polarizabilities, shows that these local field theories are valid for non-harmonic absorbers only in the weak interaction limit, and only when there exist no states with both monomers simultaneously excited (e.g. one excited vibrationally, the other electronically) that are nearly degenerate with the single excitation states and also connected to them by appreciable transition moments. Failure of the local field theories is, thus, shown to be a consequence of the non-harmonic nature of real absorbers. Using a general relation between the level-shift function and complex polarizability, a recipe is formulated for calculating the complex polarizability and spectrum of a dimer.     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.     

Exciton‐Vibrational Couplings in Homo‐ and Heterodimer Stacks of Perylene Bisimide Dyes within Cyclophanes: Studies on Absorption Properties and Theoretical Analysis

The optical properties of a series of three cyclophanes comprising either identical or different perylene bisimide (PBI) chromophores were studied by UV/Vis absorption spectroscopy and their distinctive spectral features were analyzed. All the investigated cyclophanes show significantly different absorption features with respect to the corresponding constituent PBI monomers indicating strong coupling interactions between the PBI units within the cyclophanes. DFT calculations suggest a π‐stacked arrangement of the PBI units at close van der Waals distance in the cyclophanes with rotational displacement. Simulations of the absorption spectra based on time‐dependent quantum mechanics properly reproduced the experimental spectra, revealing exciton‐vibrational coupling between the chromophores both in homo‐ and heterodimer stacks. The PBI cyclophane comprising two different PBI chromophores represents the first example of a PBI heterodimer stack for which the exciton coupling has been investigated. The quantum dynamics analysis reveals that exciton coupling in heteroaggregates is indeed of similar strength as for homoaggregates.     

An analysis of the through bond interaction using the localised molecular orbitals—III : Long range effect of lone pair orbital to the optical rotatory strength of the carbonyl n-π* transition in 3-ketopiperidines

The optical rotatory strengths of the carbonyl n-π^* transitions of (1R)-3-ketopiperidine and (1S)-3-ketopiperidine were subjected to the analysis in terms of the through-space and the through-bond interactions according to the procedure using localised molecular orbitals we proposed in the preceding papers. As a result of the present analysis, the optical rotatory strengths of the molecules were found to be influenced by the direction of the remote nitrogen lone pair orbital. This influence was found to be illustrated by the coupling between the CO group and the nitrogen lone pair orbital as well as the N-H bond localized orbital via a path containing the through-bond and the through-space interactions. That is, the positive coupling and the negative coupling paths were determined by the present analysis and the sign of the optical rotatory strength was found to correspond to the sum of the contributions of both coupling paths.     

Latin American contributions to quantum chemical topology

We survey the contributions from Latin American theoretical chemists to the field of quantum chemical topology (QCT) over nearly the last 30 years with emphasis on the developments and applications of the quantum theory of atoms in molecules (QTAIM). Applications of QCT in the fields of excited states, electron delocalization, chemical bond, aromaticity, conformational analysis, spectroscopic properties, and chemical reactivity are presented. We also consider the coupling of QTAIM with time-dependent density functional theory, the virial theorem in the Kohn-Sham method and the inclusion of electron dynamical correlation in the interacting quantum atoms method using coupled cluster and multi-configurational densities. Additionally, we describe the development of efficient algorithms for the calculation of topological properties derived from the electron density. This review is aimed not only at providing an account of the contributions to QCT in Latin America but also at stimulating guides for further progress in the field.     

Real time quantum propagation on a Monte Carlo trajectory guided grids of coupled coherent states: 26D simulation of pyrazine absorption spectrum

In this work we apply the coupled coherent states technique of quantum molecular dynamics to simulation of the absorption spectrum of pyrazine. All 24 vibrational modes are taken into account. The nonadiabatic coupling obetween the S(1) and S(2) electronic states is treated by a mapping approach that adds two extra degrees of freedom to the effective vibronic Hamiltonian. The results are in a good agreement with experiment and with previous calculations by quantum multiconfigurational time dependent Hartree and semiclassical Herman-Kluk methods.     

First-principles determinations and investigations of the electronic absorption and third-order polarizability spectra of electron donor-acceptor chromophores tetraalkylammonium halide/carbon tetrabromide

Calculations on donor-acceptor molecular pairs of tetraalkylammonium halide/carbon tetrabromide complexes are provided to investigate structure/property-related linear and nonlinear optical properties by using the time-dependent density functional theory technique coupled with the sum-over-states method. The calculated energies of the first allowed electronic transition decrease, and the nonresonant third-order polarizabilities at the THG, EFISHG, and DFWM optical processes increase progressively from [DBU-H+Br-.CBr(4) to [NPr(4)Br.CBr(4)] to [NMe(4)Br.CBr(4)]. The obtained electronic absorption spectra show a progressive red shift with increasing donor strength from Cl to I for [NR(4)h.CBr(4)] (h = Cl, Br, and I). The charge transfers from the halogen donor to the carbon tetrabromide acceptor make significant contributions to the electronic absorption spectra in the low-energy zone and the third-order polarizabilities in the nonresonant frequency region. The counterion indirectly affects the electronic absorption and third-order polarizability spectra through the interactions between the donor and acceptor.     

Geometry,Electronic Structure,and Related Properties of Dye Sensitizer： 3,4-bis[1- （carboxymethyl）-3-indolyl]- 1 H-pyrrole-2,5-dione

The geometry, electronic structure, polarizability and hyperpolarizability of dye sensitizer 3,4-bis[1-（carboxymethyl）-3-indolyl]-1H-pyrrole-2,5-dione （BIMCOOH） were studied using density functional theory （DFT） with hybrid functional B3LYP, and the electronic absorption spectra were investigated using semi-empirical quantum chemical method ZINDO-1 and time-dependent DFT （TDDFT）. The results of natural bond orbital suggest that the natural charges of the dione, indole, and acetic groups are about 0.15e, -0.29e, and 0.44e, respectively. The calculated isotropic polarizability, polarizability anisotropy invariant and hyperpolarizability are 305.4, 188.3, and 1155.4 a.u., respectively. The electronic absorption spectral features in visible and near-UV region were assigned to the π→π^＊ transition due to the qualitative agreement between the experiment and the TDDFT calculations, and the transitions of the excited states 9-11 related to photoinduced intramolecular charge transfer processes. The analysis of electronic structure and UV-Vis absorption indicates that the indole groups primarily contributed sensitization of photo-to-currency conversion processes, and the interracial electron transfer between semiconductor TiO2 electrode and dye sensitizer BIMCOOH are electron injection processes from excited states of the dyes to the semiconductor conduction band.     

Effectively doubling the magnetic field in spin-1/2-spin-1, HSQC, HDQC, coupled HSQC, and coupled HDQC in solution NMR

Pulse sequences for spin-1/2-spin-1 pair heteronuclear single quantum correlation (HSQC), heteronuclear double quantum correlation (HDQC), and coupled-HSQC, and coupled-HDQC NMR spectroscopies are outlined, and experimental realization for a (13)C-(2)H pair is demonstrated in solution state. In both the coupled versions, conditions for generation of in-phase and antiphase multiplets in either dimension are arrived at. The patterns and the intensity ratios are explained. The double quantum (2Q) experiments confirm doubling of both the shift frequency and the splitting due to coupling (to spin 1/2) of the 2Q coherence emanating from spin 1. The frequency doubling is equivalent to the corresponding single quantum (1Q) coherence at double the magnetic field strength. The coupling doubling, however, is independent of the magnetic field strength and a signature feature of the 2Q coherence. The ramification of the relative relaxation rates of 1Q and 2Q coherences is discussed.