LiH molecule

Fig. 35). The potential energy curves and the transition dipole moment are taken from [117]. The time evolution of the populations on the ground and excited states is shown in Fig. 36 More than 86% of the initial state is excited to the B state within the period shorter than a few femtoseconds. The integrated total transition probability V given by Eq. (173) is P = 0.879, which is in good agreement with the value 0.864 obtained by numerical solution of the original coupled Schroedinger equations. This means that the population deviation from 100% is not due to the approximation, but comes from the intrinsic reason, that is, from the spread of the wavepacket. Note that the LiH molecule is one of the...

The article is organized as follows. The main features of the linear response theory methods at different levels of correlation are presented in Section 2. Section 3 describes the calculation of the dipole and quadmpole polarizabilities of two small diatomic molecules LiH and HF. Different computational aspects are discussed for each of them. The LiH molecule permits very accurate MCSCF studies employing large basis sets and CASs. This gives us the opportunity to benchmark the results from the other linear response methods with respect to both the shape of the polarizability radial functions and their values in the vibrational ground states. The second molecule, HF, is undoubtedly one of the most studied molecules. We use it here in order to examine the dependence of the dipole and quadmpole polarizabilities on the size of the active space in the CAS and RASSCF approaches. The conclusions of this study will be important for our future studies of dipole and quadmpole polarizabilities of heavier diatomic molecules. 

In addition to the critical points an important feature appearing in one-electron densities are the closed contour curves corresponding to a given value of the density [20]. These closed equidensity curves envelop each one of the nuclei up to the bond critical point located along the bond path joining two nuclei. Other closed equidensity contours envelop both nuclei, etc. This is shown schematically in Fig. 2 for the LiH molecule. 

Alternatively, instead of looking for a significant truncation of the system of equations, one may try to perform multiple but simple calculations hoping for a favorable cancellation of errors. Thus, the idea tested was to start from a set of 2-TRDM s, corresponding to the eigenstates of 5, and then to apply the CLVNE in order to obtain a set of more accurate 1-TRDM s. This kind of calculation was not only carried out for the Beryllium atom but also for the LiH molecule (also with a double zeta basis set). Unfortunately, the results were not encouraging either. 

The interaction between a helium atom and the LiH molecule has been described using a SCVB wavefunction built up using just 25 structures. Interaction energies, computed along different approaches of the two moieties, compare extremely well with a corresponding traditional SCVB calculation using many more structures. Even a very small energy minimum of about 0.01 mHartree is perfectly reproduced for He at a distance of 7 =11 bohr from the centre of mass of the LiH molecule (collinear approach of He to H—Li). 

The method has been used to study the LiH system [13,14,15] for which the main interest was in the first excited state, which governs the dynamical behaviour of the neutral LiH molecule in the presence of a naked proton. Various nuclear configurations have been sampled, both in the subreactive [14] and reactive regions of the configuration space [13]. It turned out that a simple two-reference VB wavefunction was sufficient for the subreactive study, while the stretching of the LiH bond in the reactive regions required the use of an additional reference function. For this system, the ground state SC wavefunction has the form ... 

It should also be noted that the LiH molecule is one of the most difficult systems to apply the present method to, because the mass of LiH is very light at 0.875 amu and the gradient of potential difference is relatively large (V A —0.473 eV/ao) at the center of the wavepacket. All of these difficulties have been nicely overcome by employing fast quadratic chirping. This fact guarantees the usefulness of the present method. 

Much theoretical work has been carried out on the lithium hydride molecule, which has become the workbench of the theoretical chemist (J ). Browne ( ), and Fraga and Ransil ( 3) have given the binding energy for the LiH ion by ab initio calculation Com-panion(j4) has applied the diatomic-in-molecule theory to the Li H and LiH. molecules and predicted the stabilities of these molecules. We have intensively studied the Li-H system by means of Knudsen effusion mass spectrometry, and identified all predicted molecules and ions as cited above(5), and reported the thermochemical properties of these gaseous species (, 2, ) ... 

Fig. 5.16 Electron densiiy contours for LiF, HF, and LiH molecules. All molecules drawn to the same scale. The inner eontours of F in HF and Li in LiH have been omitted for eianty. [From Bader R. F. W. Keaveny. I. Cade, P. E. J. Chem. Phyx. 1967,...

On the calculation of long-range coulombic contributions to the direct space LCAO CO matrix elements of model polymers. They applied the FSGO model for an infinite chain of LiH molecules. 

In 1965 Ebbing and Henderson [25] analyzed geminals in the LiH molecule and optimized them by inspecting total energy curves as functions of orbital rotation parameters. 

The vibrational heating efficiency of LiH molecules in collisions with He atoms was the subject of further study [34], The excitation and relaxation rates over a broad range of temperatures were reported, together with the average energy transfer indices. It was found that in spite of the weak nature of the van der Waals interaction, the strong anisotropy of the surface leads to rovibrational excitation rates which are larger, for example, than those exhibited by the He-CO [35] or He-N2 [36] systems. 

The formulae for generalized few-state models for two-photon absorption with numerical illustration at the ab initio level were given by Cronstrand et al. [29], More recently, Cronstrand et al., have presented approximate expressions for three-photon absorption with application to PNA and LiH molecules [30]. 

Fig. 22.5. Plot of energy difference [A (mH) = ( pci method)] the ground state of LiH molecule using...

Table 22.2 Spectroscopic constants of LiH molecule using various basis...

First and second order electrical property LiH molecule... 

It has been found that the relatively small three-dimensional active space is sufficient to generate good values of the dipole moment and polarizability surface of the parallel component over the wide range of geometries of the LiH molecule. 

Fig. 22.13. Dipole moment function (/n ) of the ground state of LiH molecule using 631IG basis.

The Be results are reproduced in Table la similar results were found for the LiH molecule (Table Ib). A more crucial non-empirical test of the theory would be on say the neon 2p shell, on which calculations are in progress. 

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