New inversion coordinate for ammonia: Application to a CCSD(T) bidimensional potential energy surface

Abstract

A new inversion coordinate is defined for ammonia as a function of the valence angles. Its square is similar to the often used totally symmetric bending displacement coordinate for the pyramidal XY3–type molecules. We have used this in a two-dimensional calculation including the totally symmetric stretching and the inversion mode. A conventional symmetrized internal coordinate is employed for the symmetric stretch. A two-dimensional potential energy surface is calculated using the ab initio CCSD(T) method together with the aug-cc-pVTZ, cc-pVQZ, and aug-cc-pVQZ basis sets. The corresponding eigenvalues are calculated variationally using a Morse oscillator basis set for the stretch and a harmonic oscillator basis set for the inversion. A good agreement is obtained between the calculated and 22 experimental inversion levels, 9 of NH314 and the others involving 4 other isotopomers (14ND3, NH315, ND315, and NT314). With the aug-cc-pVTZ basis, a mean absolute error of 5.0 cm−1 is obtained whereas with the aug-cc-pVQZ basis set the error becomes 7.9 cm−1.

Treatment of nonlinear optical properties due to large amplitude anharmonic vibrational motions: Umbrella motion in NH3

“…While the former is clearly better for the energy levels, the latter is more accurate for the splittings. The mean absolute deviation ͑MAD͒ and maximum absolute deviation ͑MAXAD͒ obtained for the energy levels with MP2 / POL/ turns out to be better than the 1D CCSD͑T͒/aug-cc-pvTZ values obtained by Pesonen et al 55 Although the deviations are significantly larger for the MP2 / POL/ z energy levels, which are more important than inversion splittings for vibrational ͑hyper͒polarizabilities, we obtain the MP2/POL properties for z as well as in order to see how sensitive the results are to the choice of coordinate. Of course, the MAD can be reduced by increasing the dimensionality to two dimensional 55 and six dimensional [56][57][58] Indeed, our third goal is to see the effect of reducing the dimensionality.…”

Recent Advances in the Theory of Vibration–Rotation Hamiltonians

“…We find the tangent qz a =qf abg from the tangent qz a =qt abg [Eq. (58)] by performing the coordinate transformation from fz a ; y ab ; t abg g to fz a ; y ab ; f abg g. Because both coordinate sets include fz a ; y ab g, it suffices to consider f abg as function of t abg only; that is, we can write …”

Complex symmetrized calculations on ammonia vibrational levels

“…This major difficulty for the theoretical treatment requires local mode (LM) treatment, instead of the conventional normal mode (NM) analysis. The N-H stretch overtone structure at the higher excitation energies is additionally complicated through the occurence of a number of strong Fermi and Darling-Dennison resonances [2,3,21,22]. Within this range, the density of the molecular vibrational level increases to the extent that the vibrational computations become difficult and time consuming.…”

“…The quantum mechanical treatment is greatly reduced if the eigenfunctions of H when real symmetrized vibrational coordinates are used [20][21][22][23]. To derive complex symmetry adapted orthogonal N-H stretch wavefunctions ϕ corresponding to a configuration p 1 k 2 l 3 , simple linear combinations must be taken, by rotating the original configura-…”

“…For this reason, extensive spectroscopic measurements have been performed on 14 NH 3 as well as on its isotopomers [1][2][3][4][5][6], in a wide spectral range. Many theoretical studies have also been carried out to rationalize the extremely complicated NH 3 PES and ro-vibrational spectrum [2,3,[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. Ammonia is a symmetric top molecule, belonging to the point group D 3h [1,7,27].…”