Kramers

Once the imaginary part of the dielectric function is known, the real part can be obtained from the Kramers-Kronig relation ... [Pg.119]

The more conventional, energy domain fonnula for resonance Raman scattering is the expression by Kramers-Heisenberg-Dirac (KHD). The differential cross section for Raman scattering into a solid angle dD can be written in the fomi... [Pg.252]

Kramers and Wamher [103] used this to locate the critical temperature = l.llJIk. [Pg.539]

Kramers H A and Wannier G H 1941 Statistics of the two-dimensional ferromagnet part I Phys. Rev. 60 252... [Pg.556]

The real part of n , the dispersive (reactive) part of and the definition of Xy implies a relation between tr yand -/which is known as the Kramers-Kronig relation. [Pg.719]

According to Kramers model, for flat barrier tops associated with predominantly small barriers, the transition from the low- to the high-damping regime is expected to occur in low-density fluids. This expectation is home out by an extensively studied model reaction, the photoisomerization of tran.s-stilbene and similar compounds [70, 71] involving a small energy barrier in the first excited singlet state whose decay after photoexcitation is directly related to the rate coefficient of tran.s-c/.s-photoisomerization and can be conveniently measured by ultrafast laser spectroscopic teclmiques. [Pg.820]

The transition from k to on the low-pressure side ean be eonstnieted using iiiidtidimensional unimoleeular rate theory [1, 44], if one knows the barrier height for the reaetion and the vibrational frequeneies of the reaetant and transition state. The transition from to k y ean be deseribed in temis of Kramers theory [45]... [Pg.847]

Kramers solution of the barrier crossing problem [45] is discussed at length in chapter A3.8 dealing with condensed-phase reaction dynamics. As the starting point to derive its simplest version one may use the Langevin equation, a stochastic differential equation for the time evolution of a slow variable, the reaction coordinate r, subject to a rapidly statistically fluctuating force F caused by microscopic solute-solvent interactions under the influence of an external force field generated by the PES F for the reaction... [Pg.848]

This ensures the correct connection between the one-dimensional Kramers model in the regime of large friction and multidimensional imimolecular rate theory in that of low friction, where Kramers model is known to be incorrect as it is restricted to the energy diflfiision limit. For low damping, equation (A3.6.29) reduces to the Lindemann-Flinshelwood expression, while in the case of very large damping, it attains the Smoluchowski limit... [Pg.849]

In the Smoluchowski limit, one usually assumes that the Stokes-Einstein relation (Dq//r7)a = C holds, which fonns the basis of taking the solvent viscosity as a measure for the zero-frequency friction coefficient appearing in Kramers expressions. Here C is a constant whose exact value depends on the type of boundary conditions used in deriving Stokes law. It follows that the diffiision coefficient ratio is given by ... [Pg.850]

According to Kramers model, for flat barrier tops associated with predominantly small barriers, the transition from the low- to the high-damping regime is expected to occur in low-density fluids. This expectation is home... [Pg.853]

Kramers H A 1940 Brownian motion in a field of force and the diffusion model of chemical reactions Physica 7 284-304... [Pg.865]

Schroeder J, Tree J and Vdhringer P 1995 Photoisomerization of f/ a/rs-stilbene in compressed solvents Kramers turnover and solvent induced barrier shift Z. Phys. Chem. 188 287... [Pg.865]

Hanggi P, Talkner P and Borkovec M 1990 Reaction-rate theory fifty years after Kramers Rev. Mod. Phys. 62 251-341... [Pg.865]

Larson R S and Kostin M D 1982 Kramers theory of chemical kinetics curvilinear reaction coordinates J. Chem. Phys. 77 5017-25... [Pg.865]

Berezhkovskii A M, Berezhkovskii L M and Zitserman V Yu 1989 The rate constant in the Kramers multidimensional theory and th Chem. Phys. 130 55-63... [Pg.866]

Berezhkovskii A M and Zitserman V Yu 1991 Activated rate processes in the multidimensional case. Consideration of recrossings in the multidimensional Kramers problem with anisotropic friction Chem. Phys. 157 141-55... [Pg.866]

Berezhkovskii A M and Zitserman V Yu 1992 Generalization of the Kramers-Langer theory decay of the metastable state in the case of strongly anisotropic friction J. Phys. A Math. Gen. 25 2077-92... [Pg.866]

Zhu S-B, Lee J, Robinson G W and Lin S H 1988 A microscopic form of the extended Kramers equation. A simple friction model for cis-trans isomerization reactions Chem. Phys. Lett. 148 164-8... [Pg.866]

Sun Y-P and Saltiel J 1989 Application of the Kramers equation to stiibene photoisomerization in / -alkanes using translational diffusion coefficients to define microviscosity J. Phys. Chem. 93 8310-16... [Pg.867]

Borkoveo M and Berne B J 1985 Reaotion dynamios in the iow pressure regime the Kramers modei and ooiiision modeis of moieouies with many degrees of freedom J. Chem. Phys. 82 794-9... [Pg.868]

Nitzan A 1988 Activated rate processes in condensed phases the Kramers theory revisited Adv. Chem. Phys. 70 489 Onuchic J N and Wolynes P G 1988 Classical and quantum pictures of reaction dynamics in condensed matter resonances, dephasing and all that J. Phys. Chem. 92 6495... [Pg.896]

Talkner P and Hanggi P (eds) 1995 New Trends in Kramers Reaction Rate Theory (Dordrecht Kluwer)... [Pg.896]

See, for example, Poliak E 1986 Theory of activated rate processes a new derivation of Kramers expression J. Chem. Phys. 85 865... [Pg.897]

Berezhkovskii A M, Poliak E and Zitserman V Y 1992 Activated rate processes generalization of the Kramers-Grote-Hynes and Langer theories J. Chem. Phys. 97 2422... [Pg.897]

B1.3.2.5 THE MICROSCOPIC HYPERPOLARIZABILITY TENSOR, ORIENTATIONAL AVERAGING, THE KRAMERS-HEISENBERG EXPRESSION AND DEPOLARIZATION RATIOS... [Pg.1189]

B) THE MICROSCOPIC HYPERPOLARIZABILITY IN TERMS OF THE LINEAR POLARIZABILITY THE KRAMERS-HEISENBERG EQUATION AND PLACZEK LINEAR POLARIZABILITY THEORY OF THE RAMAN EFFECT... [Pg.1190]

Consider Raman transitions between thennalized molecular eigenstate g (ground) and molecular eigenstate/ (final). The quantum mechanical expression for responding to colours and j is the famous (thennalized) Kramers-Heisenbergequation [29]... [Pg.1192]

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