Calculation of Absorption Spectra

The absorption spectrum is a useful observable that can be simulated using either a time-independent or a time-dependent formalism. In the case of molecular systems exhibiting conical intersections, the strong vibronic couplings often have distinct signatures in the absorption spectrum. For instance, the presence of unexpected bands, or of bands with an unusually complicated and denseproflle, is often observed. 

Consider a molecular system described by the Hamiltonian operator H with the eigenelements 4 , E . The absorption profile is given by Fermi s golden rule 

We note that a very efficient version of this method based on the Lanczos iterative eigensolver has been implemented for the specific case of vibronically coupled systems described by the vibronic coupling model Hamiltonian, allowing for the computation of absorption or photoelectron spectra for systems with bases containing up to 10 basis functions. This method is described in details in the Chap. 7 of Ref. [64]. 

In a number of cases, it can be advantageous to compute the absorption spectrum without any reference to the eigenstates of the system but rather using the time-dependent wavepacket computed through the solution of the time-dependent Schrodinger equation. Using the integral form of the Dirac delta function, Eq. (4.55) can be recast as 

The wavepacket at time f = 0 is obtained through the application of the dipole moment operator to the initial state I (0)) = /l ,). Substituting into Eq.(4.58) yields 

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To verify effectiveness of NDCPA we carried out the calculations of absorption spectra for a system of excitons locally and linearly coupled to Einstein phonons at zero temperature in cubic crystal with one molecule per unit cell (probably the simplest model of exciton-phonon system of organic crystals). Absorption spectrum is defined as an imaginary part of one-exciton Green s function taken at zero value of exciton momentum vector... 

The methodology of molecular quantum dynamics applied to non-adiabatic systems is presented from a time-dependent perspective in Chap. 4. The representation of the molecular Hamiltonian is first discussed, with a focus on the choice of the coordinates to parametrize the nuclear motion and on the discrete variable representation. The multi-configuration time-dependent Hartree (MCTDH) method for the solution of the time-dependent Schrddinger equation is then presented. The chapter ends with a presentation of the vibronic coupling model of Kdppel, Domcke and Cederbaum and the methodology used in the calculation of absorption spectra. 

This may lead to an overestimation of electrochromic effects on neighbouring pigments. Finally the inclusion of double and triple excitations allows the calculation of absorption spectra of excited states including radical pairs and triplets. It seems feasible in the near future to make a calculation on the whole hexamer of the reaction center thereby getting access to the spectra of intermediate states including the electrochromic shifts. 

Improta, R., Barone, V., 8c Santoro, F. (2007). Ab initio calculations of absorption spectra of large molecules in solution Coumarin C15313. Ange-wandte Chemie International Edition, 46(3), 405-408. 

An important modification of this approach has been the consideration of damping of the internal electric fields due to the dipoles first proposed by Thole [38]. Extension to dynamic polarizabilities has also been arrived at and application to the calculation of absorption spectra has been reported. The dipole model has also been extended to include atomic charges induced by external field along with the internal field due to other charges and dipoles. 

Etienne T, Assfeld X, Monari A (2014) QM/MM calculation of absorption spectra of complex systems the case of human serum albumin Comp. Theoret Chem 1040-1041 360-366... 

Fig. 6. Calculated optical absorption spectra of a metallic CNT in a magnetic flux. In the case that the electric field is parallel to the axis (left), the absorption exhibits a distinct AB effect. In the case of the perpendicular polarisation (right) the depolarisation effect suppresses the absorption almost completely.

In this chapter we have shown that the dynamics and spectroscopy of the initial events taking place in bacterial photosynthetic RCs can be described by the model shown in Table I and Fig. 19. Using these physical constants we can calculate the absorption spectra, ET rate constants, and fs time-resolved spectra. It should be noted that for processes taking place in sub-ps range, it is more reasonable not to use rate constant because the concept of rate constant requires the validity of the Markoff approximation [82,88]. Instead the... 

The advent of the laser has stimulated new research in collisional physics. The term laser-assisted collision was coined to describe the various research activities that have evolved. These studies are concerned with electronic transitions in supermolecules and will be briefly considered here. Similarities between laser-assisted collisions (LAC) and collision-induced absorption (CIA) exist, both in the types of phenomena considered and in the calculations of the spectra [208]. 

Comprehensive material concerning the calculation of electronic spectra of pseudoazulenes deals with the question of whether these compounds also possess the interesting absorption properties of the azulenes. The calculations show that all unsubstituted pseudoazulenes should possess a long-wavelength electronic transition between 500 and 700 nra. corresponding to an S0 - S, transition with n,n character. For simple representatives of the [b]-series this long-wavelength transition is bathochromically shifted in the order of oxalenes to azalenes to thialenes. 

A simulation of the color variations for various mixing ratios of the dyes was performed in order to select the most suitable color variation. When the absorption spectra are obtained at a certain concentration (Cdye,o) of the dye, L a b values at various concentrations of the dye (Cdye) can be calculated. The absorption spectra A (A) at Cdye are given by the following equation ... 

A similar translation scheme from the full quantum approach to a mixed quantum classical description has been used recently in Ref. [26-29] to calculate infrared absorption spectra of polypeptides within the amide I band (note that the translation scheme has been also used in the mentioned references to compute nonlinear response functions). 

In this Chapter we describe the extension of the parametric model used for 4f" spectra to calculations of absorption and emission spectra for the 4f 15d configuration. We also illustrate how they can be applied to calculate other properties of interest, such as non-radiative relaxation rates. Finally, we discuss the relationship between parametrized calculations and other approaches, such as ab initio calculations. 

As described in earlier sections, any two material bodies will interact across an intermediate substance or space. This interaction is rooted in the electromagnetic fluctuations— spontaneous, transient electric and magnetic fields—that occur in material bodies as well as in vacuum cavities. The frequency spectrum of these fluctuations is uniquely related to the electromagnetic absorption spectrum, the natural resonance frequencies of the particular material. In principle, electrodynamic forces can be calculated from absorption spectra. 

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