Ground State of LiH

There are two electrons to place in the MO energy-level scheme for LiH shown in Fig. 2-20. This total is arrived at by adding together the one valence electron contributed by hydrogen (Ir) and the one valence electron contributed by lithium (Ir). Both electrons are accommodated in the cr MO, giving a ground-state configuration 

Since the electrons in the a MO spend more time in the vicinity of the H nucleus than of the Li nucleus, it follows that a separation of charge is present in the ground state. That is, the Li has a partial positive charge and the H has a partial negative charge, as shown below  

A limiting situation would exist if both electrons spent all their time around the H. The LiH molecule in that case would be made up of a Li+ ion and a H ion that is, S = 1. A molecule that can be formulated successfully as composed of ions is described as an ionic molecule. This situation is encountered in a diatomic molecule only if the valence orbital of one atom is very much more stable than the valence orbital of the other atom. The LiH molecule is probably not such an extreme case, and thus we say that LiH has partial ionic character. A calculation of the coefficients Ci, C2, and C3 would be required to determine the extent of this partial ionic character. One such calculation (unfortunately beyond the level of our discussion here) gives a charge distribution 

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

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

B. Chen and J. B. Anderson,/. Chem. Phys., 102,4491 (1995). A Simplified Released-Node Quantum Monte Carlo Calculation of the Ground State of LiH. 

Figure 36. Time variation of the wave packet population on the ground X and excited B states of LiH. The system is excited by a single quadratically chirped pulse with parameters 0(a, = 5.84 X 10 eV fs , = 2.319 eV, and / = 1.00 TWcm . The pulse is centered at t = 0...

General p-particle A -representability conditions on the 2-RDM are derivable from metric (or overlap) matrices. From the ground-state wavefunction lih) and a set of p-particle operators. of basis functions can be defined. 

E. HF and HF+.—The HF molecule has probably been as much studied theoretically as any other hydride except for LiH. The ground state of HF was recently investigated by Bondybey et al.137 Using extended STO basis sets, their computed SCF wavefunction gave an energy which was within 0.0028 hartree of Cade and Huo s value.104 Correlated wavefunctions were obtained by the first-order pro-... 

Table 21 Ground state of H2, LiH and HF molecules by DQMC/FSGO. (au)... 

Fig. 6.3. Contour maps of the ground-state electronic charge distributions for the second- and thrid-row diatomic hydrides showing the positions of the interatomic surfaces. The first set of diagrams (a) also includes a plot for the ground state of the Hj molecule. The outer density contour in these plots is 0.001 au. The remaining contours increase in valne according to the scale given in the Appendix (Table A2). (a) The left-hand side 2, LiH 2, BeH 2, BH 2 right-hand side CH n, NH 2", OH n, HF 2+. (b)The left-hand side NaH 2-, MgH 2+, AIH 2+, SiH right-hand side PH 2-, SH "H. HCI 2. ...

Several calculations have been reported for the AGP-based polarization propagator applied to atoms and small molecular systems. When the Eq. (5.67) is satisfied, individual stationary excited states can be obtained as excitations from the AGP reference state. Thus, starting from an energy optimized AGP, the vertical excitation (and de-excitation energies, when the AGP is not the ground state) determines potential energy surfaces and wavefunctions for other states. B. Weiner and Y. Ohrn calculate the ground state of the LiH... 

Calculations were originally carried out (2 ) for the lowest states of Hz, LiH, BH, NH, and HF and the corresponding deuterated molecules with the LCAO-MO wavefunction of Coulson for Hz (11) and the LCAO-MO-SCF functions of Hansil (12) for the other molecules. These wavefunctions contain a minimum basis set of inner and valence shell Slater-type orbitals with the orbital exponents optimized at the experimental equilibrium intemuclear distance. The S states are the ground states of the respective molecules except in the case of NH. 

Problem For LiH, the rotational constant in the ground electronic state is 7.51 cm" and the harmonic vibrational frequency is about 1400.0 cm F With a harmonic, rigid rotator treatment of vibrational-rotational states, predict the transition frequencies of the eight most intense rotational fine structure lines in the m = 0 m" = 0 vibrational band for excitation from the ground state to an electronic state of LiH with a harmonic frequency of 1100.0 cm i and (1) an excited state equilibrium bond length 8% greater than that of the ground state and then (2) 8% shorter. Take to be 22,000.0 cm-i. 

There have been a few recent studies of the corrections due to nuclear motion to the electronic diagonal polarizability (a ) of LiH. Bishop et al. [92] calculated vibrational and rotational contributions to the polarizability. They found for the ground state (v = 0, the state studied here) that the vibrational contribution is 0.923 a.u. Papadopoulos et al. [88] use the perturbation method to find a corrected value of 28.93 a.u. including a vibrational component of 1.7 a.u. Jonsson et al. [91] used cubic response functions to find a corrected value for of 28.26 a.u., including a vibrational contribution of 1.37 a.u. In all cases, the vibrational contribution is approximately 3% of the total polarizability. 

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. 

Table 2. LiH dipole and quadrupole polarizability (in atomic units) for the vibrational ground state u = 0 calculated with different response theory methods. P(Pe) is the value at the minimum of the potential energy curve, Pq o is the value in the vibrational ground state and ZPVC = Pq o P(Pe) is the corresponding zero-point-vibrational correction...

We have compared our MCSCE results for the vibrational ground state with CCSD, SOPPA, and SOPPA(CCSD) calculations. In particular we have investigated the importance of the PEC on the ZPVCs and find that there are significant differences between LiH and HF. In LiH the CCSD results for the ZPVC are very close to the MCSCF results independent on whether the CCSD or MCSCF PEC was employed. Similarly, the differences between SOPPA(CCSD) calculations with either the CCSD or the MCSCF energy surface are very small. In HF, on the other hand somewhat larger differences are found if the CCSD polarizabilities are averaged over the CCSD PEC and the difference between... 

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