The previously reported nonreproducibility of the intensity of the OH stretching band of liquid water has been explored. It was found that it can be eliminated in measurements with the Circle® multiple ATR cell by ensuring that the ATR rod is coaxial with the glass liquid holder. It was also found that normal laboratory temperature variations of a few degrees change the intensity by ⩽∼1% of the peak height. A new imaginary refractive index spectrum of water has been determined between 4000 and 700 cm1 as the average of spectra calculated from ATR spectra recorded by four workers in our laboratory over the past seven years. It was obtained under experimental and computational conditions superior to those used previously, but is only marginally different from the spectra reported in 1989. In particular, the integrated intensities of the fundamentals are not changed significantly from those reported in 1989. The available imaginary refractive index, k, values between 15,000 and 1 cm−1 have been compared. The values that are judged to be the most reliable have been combined into a recommended k spectrum of H2O(l) at 25 °C between 15,000 and 1 cm−1, from which the real refractive index spectrum has been calculated by Kramers–Kronig transformation. The recommended values of the real and imaginary refractive indices and molar absorption coefficients of liquid water at 25 ± 1 °C are presented in graphs and tables. The real and imaginary dielectric constants and the real and imaginary molar polarizabilities in this wavenumber range can be calculated from the tables. Conservatively estimated probable errors of the recommended k values are given. The precision with which the values can be measured in one laboratory and the relative errors between regions are, of course, far smaller than these probable errors. The recommended k values should be of considerable value as interim standard intensities of liquid water, which will facilitate the transfer of intensities between laboratories.

The real and imaginary refractive index spectra of mixtures of water and acetonitrile over the full composition range at 25 °C were determined between 8000 and 700 cm-1 by calibrated multiple attenuated total reflection spectroscopy. Under the assumption of the Lorentz local field, the corresponding molar polarizability spectra, αm(ν̃) = α‘m(ν̃) + iα‘‘m(ν̃), were calculated and used to investigate the structure of the mixtures. The concentrations of water-bonded, acetonitrile-bonded, and non-hydrogen-bonded O−H groups, and of water-bonded and non-hydrogen-bonded acetonitrile molecules, were obtained from the integrated intensities C OH and C CN, the areas under the O−H and C⋮N stretching bands in the ν̃α‘‘m spectra. The results indicate that no enhancement of the water structure (OH---O bonding) results from the addition of acetonitrile. In contrast, a monotonic decrease in the fraction of O−H groups that are bonded to oxygen is observed with increasing CH3CN content. At low acetonitrile concentration, x CH 3 CN ≤ 0.05, where x is the mole fraction, the total fraction of OH groups that are hydrogen bonded increases slightly with increasing CH3CN content because the formation of OH---N bonds slightly exceeds the destruction of OH---O bonds. The present results are consistent with the existence of microheterogeneity at compositions near 30−50 mol % of acetonitrile. However the fraction of OH groups that are hydrogen bonded to water is 0.50 at 50 mol % CH3CN and decreases to 0.35 at 70 mol % CH3CN. Both of these fractions are too small to support water clusters more complex than linear chains or hexagons

A new and simple procedure is presented for the calculation of the infrared real, n, and imaginary, k, refractive index spectra from s-polarized attenuated total reflection ͑ATR͒ spectra by a modified Kramers-Kronig transform of the reflectance to the phase shift on reflection. The procedure consists of two parts, first a new modified Kramers-Kronig ͑KK͒ transform, and second a new, wave number-dependent, correction to the phase shift. The procedure was tested with ATR spectra which were calculated from refractive index spectra that were synthesized under the classical damped harmonic oscillator model. The procedure is far more accurate than previous procedures for the real case of a wave number-dependent refractive index of the incident medium, and yields n and k values that are accurate to р0.1% provided that no errors are introduced by the omission of significant reflection bands. This new procedure can be used to obtain optical constants from any ATR experiment that yields the spectrum of R s , the reflectance polarized perpendicular to the plane of incidence. In this laboratory R s spectra are obtained from samples held in the Spectra-Tech CIRCLE cell in a Bruker IFS 113 V spectrometer. Accordingly the ATR spectra used to test the new procedure were calculated for the optical configuration of this system, which is m reflections at 45°i ncidence with equal intensities of s-and p-polarized light and retention of polarization between reflections. For the previously studied ͓J. S. Plaskett and P. N. Schatz, J. Chem. Phys. 38, 612 ͑1963͒; J. A. Bardwell and M. J. Dignan, ibid. 83, 5468 ͑1985͔͒, but unreal, case of constant refractive index of the incident medium, n 0 , the new transform gave better results than either of two previously studied procedures. In this case the phase shift at each wave number was corrected by a constant which ensured that the correct phase shift was obtained at the highest wave number in the transform, 7800 or 8000 cm Ϫ1 . In contrast to a previous study ͓J. Chem. Phys. 83, 5468 ͑1985͔͒ it was found that the normal KK transform is inferior for this case to a previous modified KK transform ͓J. Chem. Phys. 38, 612 ͑1963͔͒, and it is also inferior to the new modified KK transform. Further, the new transform has only the usual singularity of a KK transform, and this makes it numerically superior to the previous modified KK transform which has an additional singularity at 0 cm Ϫ1 . For the real case, in which the refractive index of the incident medium changes with wave number, the new transform was used with a new simple wave number-dependent additive correction to the phase shift. This new correction is calculated with the actual value of n 0 at each wave number. For molecular liquids such as methanol and benzene the new transform is markedly superior to the previous two transforms. It yields real and imaginary refractive index values that are accurate to better than 0.1% provided the reflection spectrum is known down to 2 cm Ϫ1 . The latter condition is rarely fulfilled, and the effect o...

This paper addresses the separation of the contributions to the visible refractive index of colorless liquids from electronic ͑ultraviolet͒ and vibrational ͑infrared͒ absorption. The goal is to find the most accurate infrared values of n el (), the refractive index that results solely from electronic absorption, by fitting and extrapolating currently available visible refractive index data. These values are needed, interalia, to improve the accuracy of infrared real refractive index spectra calculated by the Kramers-Kronig transform of infrared imaginary refractive-index spectra. The electronic molar polarizability ␣ el () is calculated from the values of n el () at wave numbers between 20 500 and 0 cm Ϫ1 . The methods are applied to ten liquids: H 2 O, D 2 O, CH 3 OH, CH 3 COOH, CH 3 CN ͑CH 3 ͒ 2 CO, CH 2 Cl 2 , C 6 H 6 , C 6 H 5 Cl, and C 6 H 5 CH 3 . The visible refractive indices are expressed as power series in wave number, by expansion of the Kramers-Kronig integral. Terms in ϩ2m , mϭ1,2, are due to the electronic contribution and terms in Ϫ2m are due to the vibrational contribution. The vibrational contribution to the visible refractive index is also calculated from experiment by Kramers-Kronig transformation of the known infrared imaginary refractive index spectrum of the liquid. It is shown that the vibrational absorption contributes у0.001 to the visible refractive index only for the four hydrogen-bonded liquids, and that, for all ten liquids, at least 25% of the vibrational contribution arises from absorption below 2000 cm Ϫ1 . If the vibrational intensities are not known, the available visible refractive indices yield the most accurate infrared values of n el for all liquids except H 2 O if they are fitted to the equation nϭa 0 ϩa 2 2 ϩa 4 4 . A similar equation, with the additional term a 2 Ϫ2 , is theoretically superior because the latter term adequately describes the vibrational contribution to the visible refractive indices, but only for H 2 O are the currently available visible refractive indices sufficiently accurate and sufficiently extensive to allow the four coefficients in the equation to be determined with useful accuracy. For H 2 O, D 2 O, CH 3 OH, CH 2 Cl 2 , C 6 H 6 , C 6 H 5 Cl, and C 6 H 5 CH 3 , corrections are given to slightly improve the accuracy of the previously published infrared real refractive-index spectra.

In this paper a multireference constant denominator perturbation theory (CDPT) is developed to reduce incomplete basis set errors arising when solving the Schrödinger equation with a finite basis set. The advantage of this method is that very few basis functions are needed, and all calculations if carried out to high enough order in the perturbation treatment effectively use a complete basis set. As a first step the theory has been restricted to one‐particle Hamiltonians and applied to the anharmonic oscillator to study the convergence properties. For perturbation calculations carried out to fifth order, results from Pade approximates show an improvement in accuracy of between one and three orders of magnitude.