In a preceding paper a one‐configuration wavefunction of strong orthogonal group functions was found to give a rather poor description of the orientation dependence of short‐range intermolecular forces in H2–H2. As an alternative to the necessity of relaxing the strong orthogonality condition, it is suggested that the introduction of a small amount of the charge‐transfer state H2−–H2+ describing one‐electron transfer between the two molecules should improve the interaction energy and its change with the relative molecular orientation. Ab initio calculations in a region of intermolecular separations ranging from two to four times the internuclear equilibrium distance of an isolated H2 molecule show that less than 1% of such a charge‐transfer state gives interaction energies which are in substantial agreement with those obtained with a complete configurational interaction.
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By restricted wavefunctions we mean here wavefunctions not allowing for the full configurational interaction proper to a given atomic basis.
6.
The “barrier” is here the difference in intermolecular energy between the two relative orientations of the two molecules defined by and
7.
The strong orthogonality condition for the many‐electron group functions and is expressed by for or both [see
R.
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, Proc. Roy. Soc. (London)
A253
, 242
(1959
)].The simplest way of ensuring strong orthogonality in a GF approach is to build and from mutually orthogonal sets of atomic orbitals.8.
9.
10.
The (singlet) Heitler‐London wavefunction can be considered as arising from the coupling to zero resultant spin of two degenerate product functions constructed from the doublet group functions describing the single electron of each atom [see R. McWeeny, Uppsala Univ. Quantum Chem. Group, Tech. Note No. 59, January 15, 1959 (unpublished)]. Here and in the following sections is worth including the normalization factor in the antisymmetrizer exchanging electrons between the two groups.
11.
The strong interconfigurational mixing between and occurs because the matrix element describing the interaction, contains large one‐electron contributions (we use here the Diracnotation and denote by 𝒽 the one‐electron Hamiltonian). At (with ) the numerical value in atomic units (see Ref. 23) resulting for the interaction is to be compared with and
12.
The one‐electron density is simply the sum of the electron densities of each group, namely
13.
When locally doubly excited configurations are admitted on each molecule the interaction is simply where J and K are the two‐electron Coulomb and exchange interactions between the pairs of transition densities and
14.
J. N.
Murrell
, M.
Randic
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The antisymmetrizer is assumed to include the normalization factor. See Ref. 10.
16.
17.
Doubly ionic states are expected to occur with extremely low weight. This view is supported by the results obtained in Part II.
18.
Each relative orientation of the two molecules possesses at least a twofold symmetry axis (see Sec. III).
19.
Both and describe an electronic state when the overall symmetry is and for
20.
21.
We thank the staff of the Computation Centre for its kind cooperation.
22.
Group functions are written as a linear combination of many‐electron basis functions consisting of Slater determinants of order and (see Sec. II). It follows then where denote many‐electron basis functions and each term in the right‐hand member merely expressing the Laplace expansion of a determinant of order according to minors from its first rows and their cofactors from the remaining rows. Hence, no matter how the electrons are partitioned between the two groups, Slater’s rules for orthonormal determinants can be used to evaluate matrix elements between generalized product functions such as
23.
Energy atomic unit length charge
24.
The iteraction energy is defined as the total molecular energy (incuding nuclear repulsion) of the composite system minus twice the ground‐state energy of an isolated hydrogen moculecul in the “Heitler‐LOndon+ionic” approximation
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© 1968 American Institute of Physics.
1968
American Institute of Physics
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