On equilibrium structures of the water molecule

Abstract

Equilibrium structures are fundamental entities in molecular sciences. They can be inferred from experimental data by complicated inverse procedures which often rely on several assumptions, including the Born–Oppenheimer approximation. Theory provides a direct route to equilibrium geometries. A recent high-quality ab initio semiglobal adiabatic potential-energy surface (PES) of the electronic ground state of water, reported by Polyansky et al. [Polyansky et al.Science 299, 539 (2003)] and called CVRQD here, is analyzed in this respect. The equilibrium geometries resulting from this direct route are deemed to be of higher accuracy than those that can be determined by analyzing experimental data. Detailed investigation of the effect of the breakdown of the Born–Oppenheimer approximation suggests that the concept of an isotope-independent equilibrium structure holds to about 3×10−5Å and 0.02° for water. The mass-independent [Born–Oppenheimer (BO)] equilibrium bond length and bond angle on the ground electronic state PES of water is reBO=0.95782Å and θeBO=104.485°, respectively. The related mass-dependent (adiabatic) equilibrium bond length and bond angle of H2O16 is read=0.95785Å and θead=104.500°, respectively, while those of D2O16 are read=0.95783Å and θead=104.490°. Pure ab initio prediction of J=1 and 2 rotational levels on the vibrational ground state by the CVRQD PESs is accurate to better than 0.002cm−1 for all isotopologs of water considered. Elaborate adjustment of the CVRQD PESs to reproduce all observed rovibrational transitions to better than 0.05cm−1 (or the lower ones to better than 0.0035cm−1) does not result in noticeable changes in the adiabatic equilibrium structure parameters. The expectation values of the ground vibrational state rotational constants of the water isotopologs, computed in the Eckart frame using the CVRQD PESs and atomic masses, deviate from the experimentally measured ones only marginally, especially for A0 and B0. The small residual deviations in the effective rotational constants are due to centrifugal distortion, electronic, and non-Born–Oppenheimer effects. The spectroscopic (nonadiabatic) equilibrium structural parameters of H2O16, obtained from experimentally determined A0′ and B0′ rotational constants corrected empirically to obtain equilibrium rotational constants, are resp=0.95777Å and θesp=104.48°.

The Case of the Weak N−X Bond: Ab Initio, Semi-Experimental, and Experimental Equilibrium Structures of XNO (X = H, F, Cl, OH) and FNO2

“…Before this correction, it is advantageous to adjust the rotational constants fitted to the observed spectrum for a small centrifugal distortion and a magnetic effect. 41,23 When the g constants needed to calculate the magnetic effect are not known, they have been calculated, with the help of the Gaussian03 36 program package, at the AVTZ B3LYP level of theory.…”

“…This procedure defines the r m (2) method. For the O-H and O-D bonds of the molecules studied, it is necessary to take into account the variation of the effective bond length upon deuteration (at equilibrium the deviation in the two bond lengths is minuscule 23 ). Watson et al 46 assumed that the apparent shortening of O-D as compared to O-H is proportional to the respective reciprocal square root of the reduced mass (m red ) of the vibrator.…”

Investigation into the subambient behavior of aqueous mannitol solutions using temperature-controlled Raman microscopy

“…PC4 represents a decrease at $3125 cm À1 against an increase from 3200 to 3400 cm À1 . Using the correlation between the O-H stretching frequency and donor bond length [30] we can determine that a higher score represents weak and medium hydrogen bonds (with donor O-H bond lengths estimated at 97.3-99.3 pm) as the loadings have positive bands at higher Raman shifts while a low score is related to strong hydrogen bonds (99.9 pm). PC5 measures the ratio of intensity at 3110 to 3160 cm À1 , which is the ratio of very strong hydrogen bonds to medium-strong hydrogen bonds (estimated donor bond lengths 100.1 and 99.6 pm).…”

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“…Cheng et al [10] measured the optical absorption spectra of H 2 O, HOD, and D 2 O in the 125-145 nm region at the room temperature using synchrotron radiation. Császár et al [11] computed the equilibrium structures of H 2 O and D 2 O by the CVRQD method. Zhang et al [12] investigated the analytical potential energy of hydrogen isotopic diatomic molecule.…”