Excitation function state-specific

Linear response function approaches were introduced into the chemistry literature about thirty years ago Ref. [1,2]. At that time they were referred to as Green functions or propagator approaches. Soon after the introduction it became apparent that they offered a viable and attractive alternative to the state specific approaches for obtaining molecular properties as excitation energies, transition moments and second order molecular properties. 

F(2P3/2) + HD, which occurs at Ec = 1.16kcal/mol, is reached, a sudden drop (growth) of the v = 2 (v = 3) branching was observed. In fact, the vibration state-specific excitation functions displayed two distinctive features a steplike feature span from 0.2 to 1 kcal/mol was detected for... 

Abstract. The development of modern spectroscopic techniques and efficient computational methods have allowed a detailed investigation of highly excited vibrational states of small polyatomic molecules. As excitation energy increases, molecular motion becomes chaotic and nonlinear techniques can be applied to their analysis. The corresponding spectra get also complicated, but some interesting low resolution features can be understood simply in terms of classical periodic motions. In this chapter we describe some techniques to systematically construct quantum wave functions localized on specific periodic orbits, and analyze their main characteristics. 

Femtosecond spectroscopic investigations in the spectral range 400-880 ran have permitted to discriminate specific OH effects on the dynamics of short lived UV excited CTTS states and transient near-IR (HO e )H20 pairs. The complex nature of ultrafast prehydration elementary redox reactions with nascent OH radical (strong acid) must be contemplated in the framework of ion-pairs dynamics, ion-solvent correlation function, short-range ordering water molecules, solvent screening or anisotropic electric field effects and short-time vibronic couplings. 

Conventional FTIR instruments, in which the interferometer mirror is translated at a constant velocity, are ideally suited to the analysis of steady state infrared emission. However, time resolution of the infrared emission is required in many applications, such as the measurement of absolute rate constants for the formation or subsequent relaxation of a vibrationally excited species. It is then necessary to follow the intensity of the emission (at a particular wavenumber if state-specific rate constants are required) as a function of time. For continuous-wave experiments, crude time resolution... 

Different electronic states have in many cases veiy differently shaped orbitals and the error introduced by using a common set cannot always be fully recovered by the MR-CI treatment. A well optimized wave function is especially important for the calculation of transition properties like the transition moments and the oscillator strength. A state specific calculation of the orbitals is more important for obtaining accurate values of the transition moments than extensive inclusion of correlation. Since excited states commonly exhibit large near-degeneracy effects in the wave function an MCSCF treatment then becomes necessary. 

When potential surfaces are available, quasiclassical trajectory calculations (first introduced by Karplus, et al.496) become possible. Such calculations are the theorist s analogue of experiments and have been quite successful in simulating molecular reactive collisions.497 Opacity functions, excitation functions, and thermally averaged rate coefficients may be computed using such treatments. Since initial conditions may be varied in these calculations, state-to-state cross sections can be obtained, and problems such as vibrational specificity in the energy release of an exoergic reaction and vibrational selectivity in the energy requirement of an endo-... 

Absorption and photodissociation cross sections are calculated within the classical approach by running swarms of individual trajectories on the excited-state PES. Each trajectory contributes to the cross section with a particular weight PM (to) which represents the distribution of all coordinates and all momenta before the vertical transition from the ground to the excited electronic state. P (to) should be a state-specific, quantum mechanical distribution function which reflects, as closely as possible, the initial quantum state (indicated by the superscript i) of the parent molecule before the electronic excitation. The theory pursued in this chapter is actually a hybrid of quantum and classical mechanics the parent molecule in the electronic ground state is treated quantum mechanically while the dynamics in the dissociative state is described by classical mechanics. 

The state-specific method solves the nonlinear Schrodinger equation for the state of interest (ground and excited state) usually within a multirefence approach (Cl, MCSCF or CASSCF descriptions), and it postulates that the transition energies are differences between the corresponding values of the free energy functional, the basic energetic quantity of the QM continuum models. The nonlinear character of the reaction potential requires the introduction in the SS approaches of an iteration procedure not present in parallel calculations on isolated systems. 

S. Comi, R. Cammi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution within continuum solvation models Investigating the discrepancy between state-specific and linear-response methods, Formation and relaxation of excited states in solution A new time dependent polarizable continuum model based on time dependent density functional theory. J. Chem. Phys. 123, 134512 (2005)... 

R. Improta, V. Barone, G. Scalmani, M.J. Frisch, A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution. J. Chem. Phys. 125, 054103 (2006)... 

If the lifetime of the excited resonance state is too long for direct measurement of the rate via the widths of the spectral features, one can use a third laser (the probe laser in Fig. 11) to resonantly promote the molecules from this level to a rovibrational level in the excited electronic state. The decrease of the total LIF signal as function of the delay time between pump and probe laser reflects the state-specific dissociation rate. The limitation of the SEP technique is that an excited state has to be found, which lives long enough and which is accessible by all three lasers. Molecules, which have been studied by SEP spectroscopy in the context of unimolecular dissociation, are HCO, DCO, HFCO and CH3O. 

PSD s. They are reflections of the underlying wave functions, their nodal structures, and the dynamics in the exit channel. As outlined in detail in Ref. 20 (Chapters 9 and 10), in many cases the wave function at the TS defines the starting conditions for the final step of the fragmentation process If the system shows mode specificity, the PSD s also will show qualitative behaviors which are typical for excitation of particular modes. However, if the dissociation rates show statistical state-specific behavior, it does not necessarily follow that the PSD s have a statistical dependence on the quantum numbers of the fragments. An illuminating example is the dissociation of H2CO to be discussed in 7.3. 

Abstract. We have calculated the scalar and tensor dipole polarizabilities (/3) and hyperpolarizabilities (7) of excited ls2p Po, ls2p P2- states of helium. Our theory includes fine structure of triplet sublevels. Semiempirical and accurate electron-correlated wave functions have been used to determine the static values of j3 and 7. Numerical calculations are carried out using sums of oscillator strengths and, alternatively, with the Green function for the excited valence electron. Specifically, we present results for the integral over the continuum, for second- and fourth-order matrix elements. The corresponding estimations indicate that these corrections are of the order of 23% for the scalar part of polarizability and only of the order of 3% for the tensor part... 

Fig. 2.21. (a) Time-resolved LIF decay profiles for two closely spaced rotational levels of vibrationally excited CH3O (X). The solid line is an exponential fit for the decay convoluted with the dump laser pulse shape function, (b) Measured state specific unimolecular dissociation rate constants for CH3O (X) compared to calculated k E, J) curves without and with tunneling corrections. 

Liu, K. Excitation functions of elementary chemical reactions a direct link from crossed-beam dynamics to thermal kinetics Int. Rev. Phys. Chem. 2001, 20, 189-217. Liu K. Crossed-beam studies of neutral reactions state-specific differential cross sections. Annu. Rev. Phys. Chem. 2001, 52, 139-159. 

It is worth pointing out that the idea of searching directly for a state-specific solution for the wavefunctions of multiply excited states (MES) implies projections on distinct function spaces with separate optimization of some type, thereby avoiding serious problems having to do with the undue mixing of states and channels of the same symmetry. This idea has since been a central element of our analyses and state-specific computations. In fact, in recent years, such concerns have led to appropriate modifications of conventional methods of quantum chemistry, such as perturbation or coupled-cluster. 

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