Transition densities

One of the primary features of the Gay-Berne potential is the presence of anisotropic attractive forces which should allow the observation of thermally driven phase transitions and this has proved to be the case. Thus using the parametrisation proposed by Gay and Berne, Adams et al. [9] showed that GB(3.0, 5.0, 2, 1) exhibits both nematic and isotropic phases on varying the temperature at constant density. This was chosen to be close to the transitional density for hard ellipsoids with the same ellipticity indeed it is generally the case that to observe a nematic-isotropic transition for Gay-Berne mesogens the density should be set in this way. The long range orientational order of the phase was established from the non-zero values of the orientational correlation coefficient, G2(r), at large separations and the translational disorder was apparent from the radial distribution function. 

A system of particles interacting in this way was studied using a microcanonical ensemble at a scaled density of 3.0 which is close to the transitional density for hard oblate ellipsoids with the same ellipticity (see Fig. 3). At a scaled density of 3.0 the system is found to exhibit isotropic. 

In Fig. 1 are shown the one-center and two-center components of transition densities for some selected molecules. From these data the actual types of the most soft nuclear displacements will be deter-... 

In order to seek the most soft nuclear deformation in an excited state, the approximation is again made of replacing the sum over excited states in Eq. (17) by a dominant term corresponding to the next higher excited state. Now, the transition density p between the nth excited state corresponding to the orbital jump and the mth... 

Figure 5. The INDO/S transition densities for four conformers of Si2QH<2 (G = gauche, T = trans) in terms of the hybrid orbital basis set (contributions from Si-H bonds are negligible). Coefficient sign (bar color) and magnitude (bar length) are shown for each Si atom (circle). (Reproduced from Ref. 19. Copyright 1986 American Chemical Society.)...

Czader A, Bittner ER (2008) Calculations of the exciton coupling elements between DNA bases using the transition density cube method. J Chem Phys 128 035101... 

Krueger, B. P., G. D. Scholes, and G. R. Fleming. 1998. Calculation of couplings and energy-transfer pathways between the pigments of LH2 by the ab initio transition density cube method. J. Phys. Chem. B 102 5378-5386. 

Valleau, J. P. The Coulombic phase transition density-scaling Monte Carlo. J. Chem. Phys. 1991, 95, 584-589... 

The magnitude of the activated transition is denoted by I, where I=cN and c is an arbitrary constant. A transition density function is introduced to describe the viscoelastic and plastic shear deformation of the domain. Hence, following Eq. 107 the total shear strain of a domain in terms of the ERT model is given by... 

As an approximation it is assumed that At<2g or r(f) ==Aftan0. Furthermore the high-strain approximation for the transition density function will be ap-plied,viz. I(U)=I0 on the interval [[70, C7m] and I(U)=0 elsewhere [10]. Equation 129 then yields... 

It can be shown that for o>2 GPa a constant transition density function I=I0 yields almost the same stress dependence of the creep rate as the linear function. Therefore, in order to keep the calculations tractable we derive the lifetime of a fibre by applying the same density transition function as was used in the calculation of the dependence of the strength on the load rate, viz. I(U)=IQ on the interval [U0, Um and I(U)=0 elsewhere. This results for the shear strain of a domain in... 

Giant dipole resonance. Isovector giant resonances contain information about the SE through the restoring force. In particular the excitation of the isovector giant dipole resonance (GDR) with isoscalar probes has been used to extract A R/R [32], In the distorted wave Bom approximation optical model analysis of the cross section the neutron and proton transition densities are needed as an input. For example, in the Goldhaber-Teller picture these are... 

When rh rfi, this expression defines an element of the p-order transition density matrix (p-TRDM) [2]. In what follows when T = T, one instead of two upper indices denoting th will be used. 

Here, is the transition density and p r) is the static ground state density of valence electrons. 

It is seen from (60)-(61) that there are two alternative ways to calculate the density variation i) through the transition density and matrix elements of Qfc-operator and ii) through the ground state density. The second way is the most simple. It becomes possible because, in atomic clusters, Vres has no T-odd Ffc-operators and thus the commutator of Qk with the full Hamiltonian is reduced to the commutator with the kinetic energy term only ... 

The case of responses is more involved in the sense that matrix elements of the second operator in the commutator are transition densities which are generally complex. However, the first operator in the commutator still has real (for T-even A) or image (for T-odd A) matrix elements and so the averages can be finally reduced to... 

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