Electronic Structure of LiH Ion

Abstract

A valence-bond calculation has been carried out for (LiH)+ with all twenty structures possible from Slater orbitals 1s, 2s, 2p on lithium and 1s(=1h) orbital on hydrogen. The total electronic energy computed for the ion at the equilibrium distance for the LiH molecule is — 209.50 ev with only the 1s21h structure making a significant contribution to the ground state. When this energy is combined with the corresponding calculated energy for the molecule, a vertical ionization energy of 7.52 ev is obtained. No experimental value has as yet been reported. A technique is developed and is used to obtain the optimum orbital exponents for 1s21h over a wide range of internuclear distance. This calculated energy vs distance curve has no minimum suggesting that (LiH)+ is unstable with respect to dissociation. At R=3.08 au the wave function is ``degenerate,'' that is, two different extremum sets of exponents yield the same energy. The principal difference is that the orbital exponent of the 1h function is 0.49 in one set and 1.04 in the other. At R>3.08 au the second set gives the lowest energy while the reverse is true for R<3.08 au. This is interpreted as representing the promotion 1s→2s as is required in approaching the united atom.

Spin-free wave functions for small molecules

“…( See Appendix 1 for a description of the numerical process).The form of the wave function reflects the dissociation product where we obtain the Lithium ion and a separate Hydrogen atom as expected for large R. The sign of b is not predetermined but for all R we have the constraint a > 0 so that the wave function is normalisable .The results are presented in table 2.The pattern of the results follows previous calculations using valence bond theory with many terms [4] and large scale density function calculations [5]. We list the results in the special case a = b and for the more general case ( see Appendix 1 for the details of the approximation of the two-electron integrals and of the partial optimisation).In [4] an equilibrium is not found but a very shallow minimum is found in the more recent calculation in [5]. Our more general trial function indicates such a minimum at R about 4-5 atomic units and describes the important physical features of the wave function.…”

“…(In general this involves integration over three N variables, but the number of variables used is reduced in the examples below where the trial functions are independent of the azimuthal angles.) This follows from T 2 =T and that for arbitrary functions g and f In the case N=4 there are three physically allowed partitions: [2, 2], [3,1] and the completely antisymmetric partition [4]. Calculations in this paper are carried out for LiH and we use the same core representation as for N=3, constructed from an approximation of the ground state of (Li + +H + ), and the core function is symmetric in the interchange of the two electrons so that the partition [4] is not appropriate.…”

“…Furthermore,integrals involving only the orbitals not being optimised can be calculated prior to the optimisation. In [4] it was found necessary to use approximate, pre-calculated, values of the two-electron integrals so as to increase the speed of the optimisation. A similar technique is possible with our method by choosing how many terms are used in the Neumann expansion.…”

“…In the case N = 4 there are three physically allowed partitions: [2, 2], [3, 1] and the completely antisymmetric partition [4].Calculations in this paper are carried out for LiH and we use the same core representation as for N = 3 constructed from an approximation of the ground state of (Li + + H + ) and the core function is symmetric in interchange of the two electrons so that the partition [4] is not appropriate. The remaining electrons can be classified as valence electrons and an approximation using just these two electrons with complete shielding of the core is also symmetric in these two electrons.…”

Stability and structure of LinH molecules (n=3–6): Experimental and density functional study

“…The first generation power reactors are expected to operate by means of the deuteriumtritium fusion reaction, and tritium can be bred by reaction of neutrons with Li. 3 Early theoretical work indicated that LiH ϩ would be unstable, 4 but later calculations 5 led to a dissociation energy of up to 0. 15 9 They presented an interpretation of the latter on the basis of ab initio calculations.…”