Bond centred functions

For many-electron systems the C02 has been taken as a prototype(80). Using a basis set containing higher harmonics on the nuclear centres, together with bond centred functions originally developed for JV2 and later applied to CO as a universal basis set, a molecular basis set was developed for CO2 which may be designated... 

Some care was required in the control of computational linear dependence, which was achieved by deleted diffuse, bond centre functions. It is suggested that a total Hartree-Fock energy of an accuracy comparable with that obtained for the CO molecule was thereby achieved. 

Btiilding on atomic studies using even-tempered basis sets, universal basis sets and systematic sequences of even-tempered basis sets, recent work has shown that molecular basis sets can be systematically developed until the error associated with basis set truncation is less that some required tolerance. The approach has been applied first to diatomic molecules within the Hartree-Fock formalism[12] [13] [14] [15] [16] [17] where finite difference[18] [19] [20] [21] and finite element[22] [23] [24] [25] calculations provide benchmarks against which the results of finite basis set studies can be measured and then to polyatomic molecules and in calculations which take account of electron correlation effects by means of second order perturbation theory. The basis sets employed in these calculations are even-tempered and distributed, that is they contain functions centred not only on the atomic nuclei but also on the midpoints of the line segments between these nuclei and at other points. Functions centred on the bond centres were found to be very effective in approaching the Hartree-Fock limit but somewhat less effective in recovering correlation effects. 

The bond-centred basis functions, designated (be), are located at the point... 

Two fiu-ther types of centre on the axis passing through the nuclei are introduced -the bond-axis functions, designated (ba), lie midway between the (ac) and (be) centres having the coordinates... 

The addition of off axis basis functions in the plane perpendicular to the internuclear axis and passing through the bond centre to an axis basis set consisting of both atom-centred and bond-centred basis functions. The differences between the calculated and exact energy values are given in parentheses. 

Indeed, a number of authors have advocated the use of basis functions located at the bond centre in both self-consistent fields and in calculations... 

In the present work, the highest symmetry type included on the atomic centres are /-type functions, whilst on the bond centre symmetries up to and including d are employed. 

The bond centre subsets of -type functions are shown in Table 5. In the original subset there are 27 functions the 3 most diffuse functions being deleted from the 30 set so as to alleviate computational linear dependence problems. The number of functions truncated when applying the condition (5) is greater than for either the 5-centred or the F-centred sets reflecting the absence of a charge for this centre. For there are just 14. y-type function and this number is further reduced to 12, 8 and 4 functions for T5, T4 and T3, respectively. 

Table 5 The basis subsets of s-type functions centred on the bond centre, Stcis)...

Figure 8.6 The effect on wave-functions of inverting the electron coordinates through the centre of the molecule, The bonding wave-function is unchanged by this process but the antibonding wavefunction changes sign...

Figure A10.3 The (a) 1 (Xg+> and (c) 2(j ) wavefunctions of H2. These functions are plotted along the line of the Coo ax/s with the bond centre at the origin. The H—H distance is set at 2.00 bohr, which is the observed value from Table .1. The dotted line shows the atomic Is function of the atom to left of centre. The other two diagrams show the integrated density for planes perpendicular to the Z-direction plotted against z, with (b) representing (1 and (d) (2ffu+ 2(ru+).

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