Inverse Power Law for Complete Basis Limit of CCSD(T) Theory for OH Vibrational Potential Energies of Water Molecules

Abstract

Quantum chemical electronic energy of a molecular system depends on the level of the employed basis functions. The inverse power laws describing the convergences of the calculated Hartree-Fock (HF) and electronic correlation energies of water molecules have been determined by fitting the energies predicted by the CCSD(T) theory with various levels of correlation consistent basis functions. The law was applied to calculate the energies of a few simple water clusters by varying the OH bond distance of a molecule in order to understand how the two parts of the potential energy subject to the stretching motion of water molecules depend on the variation of local environments. It is found that the HF energy strongly depends on the environments of a local OH bond while the correlation energy is almost insensitive to the neighboring molecules. This suggests that the HF theory may have a great advantage in saving computation time for efficient calculations of vibrational frequencies widely distributed due to the inhomogeneity in the local environments of water molecules in the condensed phases.

A strategy to compute quantum chemical potential energies of inhomogeneous OH bonds in water molecules

“…26 As the cardinal number X of the basis set increases, the electronic energies predicted by a theory should converge to a CBS limiting value. However, it is well known that the rates of the convergence are different in the two types of electronic energies, HF and electron correlation (EC) energies, 27,28 the latter of which is evaluated by subtracting HF energy from CCSD(T) energy. Therefore, we considered the HF and EC energies, separately.…”

“…For each of the 10 atomic arrangements, the two types of calculated energies were assumed to independently approach their limiting values satisfying the following exponential laws as the cardinal number X increases from two to six 27,28 :…”

What Function Is Optimal for CCSD(T) Complete Basis Extrapolation for OH Stretching Potential of Water Molecules?

“…Since it is known that the two energies converge with the size of basis set to their limiting values at different rates, 16 the extrapolation schemes should be developed separately for the two energies. We will consider three functional forms found from the literature [17][18][19][20][21][22] describing the convergence behavior:…”

“…Since it is known that the two energies converge with the size of basis set to their limiting values at different rates, the extrapolation schemes should be developed separately for the two energies. We will consider three functional forms found from the literature describing the convergence behavior: and determine which of them is the best law for the potential curve of OH stretching in water molecules. Here, E ( X ) denotes the HF or correlation energy calculated by the CCSD(T) theory with aug‐cc‐pVXZ basis set of a cardinal number X and E 0 is a floating parameter pretending to be an energy in the CBS limit.…”