Dimension of discrete variable representation for mixed quantum/classical computation of three lowest vibrational states of OH stretching in liquid water

2017

Self Cite

A procedure to calculate the complete basis set limits of electronic energy of water molecules is developed based on two levels of extrapolation scheme. A three-point fitting scheme with the energies computed at the levels of basis function, aug-cc-pVXZ for X = 4-6, is employed to obtain accurate energies of a monomer and a dimer of water. Three extrapolation functions considered in this article are found to work excellently to give accurate Hartree-Fock (HF) energies of water molecules. However, the three functions give slightly different values up to 1-2 mHartree for the complete basis limit of electronic correlation energy. The best performing extrapolating function for the five-point fitting scheme with a larger set of basis functions for X = 2-6 has been determined aiming for the extrapolation from the lowest two levels of basis sets, double and triple zeta basis functions. For this purpose, an exponential function is suggested for HF energy while an exponential function with a square root exponent is suggested for electronic correlation energy. The optimal exponents of the two functions have been determined.

Section: Extrapolating Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

2017

Self Cite

“…Theories accurately predicting the frequencies that vary with the change of the HB strength are useful for quantitatively understanding those experimental results. In particular, the frequency must be calculated with properly reflecting the anharmonicity of the vibration amplified due to hydrogen bonding, as well as the nonequilibrium states of the surrounding environment.…”

Section: Introductionmentioning

confidence: 99%

“…The transition frequencies between those states are denoted as ω nm ≡ ( ε m − ε n )/ℏ. For the chemical bonds with a typical anharmonicity including the OH bonds, it has been shown that the potential energies at the ten bond lengths are necessary to effectively calculate the three vibrational energies using the numerical discrete variable representation (DVR) method . If the displacement of vibration coordinate from its equilibrium value is denoted as Q , the ten grid points required for the DVR method is given by

Q_{i} = \sqrt{\frac{normalℏ}{italicμω}} q_{i}

, where

μ^{- 1} = m_{{normalO}^{'}}^{- 1} + m_{H}^{- 1}

is the reduced mass of the pseudo‐diatomic molecule and an arbitrary angular frequency ω is set to be ω /2 πc = 3700 cm −1 for the OH bonds.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Anharmonic Stretching Frequencies of Local OH Bonds in Water Dimer: Ab Initio Potential Energy and Discrete Variable Representation

Jeon

2018

Self Cite

The fundamental and first overtone transition frequencies of local OH bonds of the hydrogen bond donor molecule in a water dimer were calculated by numerically solving one-dimensional Schrödinger equation with anharmonic potential energies obtained by ab initio quantum chemical methods at the near basis set limit. Among the various ab initio theories considered, the coupled cluster theory is found to give the most accurate frequencies in comparison with experiments, and the quadratic configuration interaction theory exhibits a similar accuracy. The calculated frequencies of the free and hydrogen-bonded OH bonds excellently agree with experimental frequencies of a gaseous dimer. It was found that the anharmonicity of the fundamental transition frequency is influenced by hydrogen bonding to a larger extent than the anharmonicity of the 1-2 transition frequency.

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

Jeon

2017

Self Cite

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.