This article describes the parameterization and performance of MMFF94 for molecular geometries and deformations. It defines the form used for the valence-coordinate terms that represent variations in bond lengths and angles, and it describes the derivation of quadratic force constants from HF/6-31G* data and the derivation of reference bond lengths and angles from fits to MP2/6-31G*-optimized geometries. Comparisons offered show that MMFF94 accurately reproduces the computational data used in its parameterization and demonstrate that its derivation from such data simultaneously confers the ability to reproduce experiment. In particular, MMFF94 reproduces experimentally determined bond lengths and angles for 30 organic molecules with root mean square (rms) deviations of 0.014 A and 1.2°, respectively. MM3 reproduces bond angles to the same accuracy, but reproduces experimental bond lengths more accurately, in part because it was fit directly to thermally averaged experimental bond lengths; MMFF94, in contrast, was fit to (usually shorter) energy-minimum values, as is proper for an anharmonic force field intended for use in molecular-dynamics simulations. The comparisons also show that UFF and a recent version of CHARMm (QUANTA 3.3 parameterization) are less accurate for molecular geometries than either MMFF94 or MM3. For vibrational frequencies, MMFF94 and MM3 give comparable overall rms deviations versus experiment of 61 cm−1 and 57 cm−1, respectively, for 15 small, mostly organic molecules. In a number of instances, MM3's derivation employed observed frequencies that differ substantially—by nearly 400 cm−1 in one case—from other published frequencies which had themselves been confirmed theoretically by good-quality ab initio calculations. Overall, the comparisons to experimental geometries and vibrational frequencies demonstrate that MMFF94 achieves MM3-like accuracy for organic systems for which MM3 has been parameterized. Because MMFF94 is derived mainly from computational data, however, it has been possible to parameterize MMFF94 with equal rigor for a wide variety of additional systems for which little or no useful experimental data exist. Equally good performance can be expected for such systems. © John Wiley & Sons, Inc.

Merck Molecular Force Field. III. Molecular Geometries and Vibrational Frequencies for MMFF94

This paper describes the observation and computer simulation of the rotational Raman spectrum of water vapor and the measurement of the depolarization ratio for Rayleigh scattering from water vapor, which was found to be (3.0±1.4) ×10−4. These results were combined with the value of the mean polarizability to calculate the principal polarizability components of the water molecule. At 514.5 nm, they are (in units of 10−24 cm3): αxx=1.468±0.003, αyy =1.415±0.013, and αzz=1.528±0.013, where the x axis is the dipole axis and the y axis is perpendicular to the molecular plane.

The Rayleigh depolarization ratio and rotational Raman spectrum of water vapor and the polarizability components for the water molecule

The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.

The anharmonic force field of ethylene, C2H4, by means of accurate ab initio calculations

The photographic technique of recording high-resolution Raman spectra of gases allows the precise measurement of wavenumber shifts and the accurate determination of molecular constants derived therefrom The corresponding methods and results are treated in Chap3 for pure rotational and in Chap2 for rotational-vibrational Raman spectra

Raman Scattering Cross Sections in Gases and Liquids

Ground states of molecules: Part XLII. Vibrational frequencies of isotopically-substituted molecules calculated using MINDO/3 force constants

From an investigation of the rotational Raman spectrum of ethylene, single transitions were assigned which allowed the determination of all three rotational constants: A0= 4.8666± 0.0040 cm–1, B0= 1.00076± 0.00013 cm–1, C0= 0.828 48± 0.000 16 cm–1.The spectrum was also computer simulated using an asymmetric rotor programme and, from a comparison of observed and calculated spectra, values were determined for the principal polarisabilities of the molecule: αzz= 5.40 A3, αxx= 3.86 A3, αyy= 3.40 A3.

Raman spectra of asymmetric top molecules. Part 1.—The pure rotational spectrum of ethylene

A detailed analysis of the Raman-active v 1, v 3 (both A-type) and v 5 (Bc -type) vibration-rotation bands of ethylene is presented In addition to structural data simulation of the spectra yields values for the polarizability ratios of the totally symmetric bands, giving information on the polarizability ellipsoid as the molecule vibrates v 3 is shown to be perturbed by a c-type Coriolis interaction which complicates the interpretation of the negative value of the polarizability ratio required to match the observed spectrum The effects of asymmetry are pronounced; one result being the formation of heads in the R,PR K p and R,P P K p branches of low K p in the v 5 band

Raman spectra of asymmetric top molecules

This paper describes and illustrates the characteristic types of rotational fine structure found in vibrational Raman bands of asymmetric top molecules. The first section contains a brief summary of the relevant theory leading to a formulation of the selection rules governing Raman spectra of asymmetric tops. They are presented in a concise, comprehensive and more useful form than hitherto. This is followed by a brief description of computer programmes which accurately simulate such Raman vibration-rotation band contours and enable individual transitions to be assigned. The final section illustrates the different band structures which can occur, namely, A, Ba, Bb, and Bc types, with possible mixtures of these in molecules of low symmetry. Attention is drawn to how information on the derivatives of elements of the polarizability tensor with respect to particular normal coordinates can be extracted from such spectra. Examples are given for ethylene and trans-1,2-dideuteroethylene.

Raman spectra of asymmetric top molecules: Part IV. Vibration-rotation selection rules and general band contours

Relocation of the ν5 fundamental vibration of ethylene-H4

ΔK= 2 transitions have been observed in the pure rotational Raman spectrum of butadiene. Rotational constants were determined for the ground state, ν13 torsional mode, ν24 bending mode and the 2ν13 torsional state. Evidence of a Coriolis interaction between ν13 and ν24 was found and the rotational constants derived from those two states were corrected for this specific interaction. A–text-decoration:overlineB values obtained for the four states were 1.247 82 ± 0.000 09 cm–1, 1.226 70 ± 0.000 24 cm–1, 1.2703 ± 0.0010 cm–1 and 1.167 ± 0.002 cm–1 for the ground, ν13, ν24 and 2v13 vibrational states respectively. In addition DK distortion constants of (3.61 ± 0.18)× 10–6 cm–1 and (2.6 ± 0.5)× 10–6 cm–1 were determined for the ground and ν13 states respectively.

G. W. Hills

Papers

Raman spectra of asymmetric top molecules. Part 1.—The pure rotational spectrum of ethylene

Raman spectra of asymmetric top molecules

Raman spectra of asymmetric top molecules: Part IV. Vibration-rotation selection rules and general band contours

Relocation of the ν5 fundamental vibration of ethylene-H4

Raman spectra of asymmetric top molecules. Part 2.—ΔK=± 2 transitions in the rotational spectrum of butadiene