First-order electrostatic energy

Equation (32) represents the first-order electrostatic energy, whereas equations (33), (34) represent the second-order contributions for the induction and dispersion energies, respectively Ers = closed-shell neutral atoms, then the electrostatic and induction energies vanish for large values of r, and the dispersion energy is the first nonzero term of the interaction energy. 

The first-order electrostatic energy is now the expectation value of the operator (14) over the molecular wavefunction, i.e. 

The first-order electrostatic energy has already been shown to arise from the Coulomb... 

Using this form of the interaction energy operator, the first-order electrostatic energy can be written as... 

Fig. 20.3 The total intermolecular interaction energy and the first-order electrostatic interaction for 54 structures of guanine-adenine complex...

The antisymmetrizing operator also affects the form of the electrostatic, induction, and dispersion energies. For example, in the case of neutral, spherically symmetric systems, the electrostatic and induction energies (which vanish in the limit of negligible orbital overlap) display a dependence on r similar to the first-order exchange energy,67... 

The first-order polarization energy, often referred to as electrostatic energy, is... 

According to SAPT formulation of the first-order interaction energy, the Heitler-London term consists of electrostatic and exchange contributions (the former obtained from the perturbation theory formula) ... 

For multi-molecular assemblies one has to consider whether the total interaction energy can be written as the sum of pairwise interactions. The first-order electrostatic interaction is exactly pairwise additive, the dispersion only up to second order (in third order a generally small three-body Axilrod-Teller term appears [73]) while the induction is not at all pairwise it is non-linearly additive due to the interference of electric fields from different sources. Moreover, for polar systems the inducing fields are strong enough to change the molecular wave functions significantly. 

The first order, electrostatic, interaction energy is defined as ... 

If all orientations were equally probable, the average potential energy (V), and hence the first-order electrostatic C3 coefficient (Magnasco 2007, 2009a Magnasco et al., 1988), would be zero. In fact ... 

One can see that for typical hydrogen bonds, O-H- -O and F-H- -O for dimer of water and the FH OCH2 complex, respectively, the electrostatic term is the most important attractive term. In all of these cases the electrostatic term outweighs the exchange term, and hence the first order interaction energy component is negative. This is again in line with conditions that the H-bond is predominantly an electrostatic interaction. Table 4 contains also the... 

The difference between the converged multipole expansion of the electrostatic energy and is sometimes called the first-order penetration energy. The exchange-repulsion is often simply called the exchange energy. For Hartree-Fock monomer wavefunctions, g l can be divided cleanly [69] into attractive exchange and... 

The first order energy is the same as given by the usual Moller-Plesset treatment, < 0 H 0 > and the first order electrostatic contribution to the free energy of solvation is identical to the result obtained at the Hartree-Fock level of flieory. The second order correction to the free energy is given as... 

Here the first-order perturbed energy is called the electrostatic energy E ... 

Here the first order interaction energies ug, ug + ug - the electrostatic energies of the corresponding charge distributions of zeroth order they ... 

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