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trend in the collection of accurate data, especially for molecular crystals (as will be evident in that section below), is the use of temperatures far below that of liquid nitrogen, involving liquid helium cryostats. Luger'' has described some of the advantages and disadvantages of closed cycle cryostats (T N 20 K) versus gas stream devices (T N 100 K), along with several applications to structural and electron density studies on several low-melting compounds. Coppens et a l l 9 have described the use of carbon composite cryostat chambers as an alternative to beryllium chambers for very low-temperature studies. The extension of X-ray diffraction and electron density studies to excited electronic states has been reported by Pressprich, White, and Coppens,20. 21 and represents a significant development. The application to a metastable state of sodium nitroprusside has also been reported in Analysis of Data, Model Studies, and Algorithms.-Su and cop pen^^^ have presented algorithms for computing the electrostatic potential, electric field, and electric field gradient from multipole expansions of the experimental electron density. Although their presentation focuses on the formalism developed by Hansen and cop pen^,^^ it can be readily modified. Su and Coppens have also reported algorithms for associated integral^,^^ normalization factors for cubic harmonic density functions26 and the rotation of real spherical harmonics,27 and the application of these methods to deuterated benzene, L-alanine, and D, L-histidine.28 The computation of the electrostatic potential from multipole models has also been presented in detail by Ghermani, Lecomte, and Bouhmaida," De Ranter and c o -w o r k e r ~, ~~ as well as by Stewart and C r a ~e n , ~' the latter presenting a general and particularly lucid description.We have discussed elsewhere the determination of electric field gradients from X-ray data32 and demonstrated the use of several different strategies, involving both direct and reciprocal space approaches, for corundum and deuterated benzene. We concluded that the successful determination of these properties from Xray data is within reach, especially for H atoms, although more flexible pseudoatom models are probably required.Several papers have also attempted the determination of potential-derived (PD) charges from experimental electrostatic potentials. PD charges are commonly used in molecular simulation studies and the X-ray experiment offers the possibility of obtaining realistic charges for molecules in the crystal. Ghermani, Bouhmaida, and

backpolarization) of the N( 1) atom in order to balance the forces that act on its n~c l e u s . '~J~ It has been found that a decrease in the value of V2p(r) at Mb results in an increase in ~a l u e '~J~ at Mnb (the N "lone pair"). Then, the observed increase in the NQCC of N( 1) when the neighboring C is substituted by a N atom is the result of the backpolarization of the N( 1) valence ~h e l l '~J~ that increases Mnb. Acknowledgment. We want to thank the CONICIT of Venezuela for partial support and to the Centro Cientifico of IBM de Venezuela C.A. for a generous grant of computer time.Ab initio calculations have been performed using mixed basis sets on two clusters carefully designed to model bulk corundum. Computational results on the clusters are compared with crystal Hartree-Fock results and with experiment for the deformation electron density and for the electric field gradient at the oxygen nucleus. Inclusion of polarization functions on central oxygen atoms in the clusters results in quantitative agreement with electron distributions derived from X-ray diffraction data. Although none of the ab initio cluster results for the oxygen electric fEld gradient tensor agree well with the experimental NMR values, agreement improves with increased basis set flexibility and better design of the cluster.A computational scheme recently proposed for ab initio calculations of electronic spectra of molecular systems is applied to the azabenzene molecules. The method has the aim of being accurate to better than 0.5 eV for excitation energies and is expected to provide structural and physical data for the excited states with good reliability. Applications are possible to molecules with up to about 20 atoms with good quality basis sets. The scheme is based on the complete active space SCF method (referred to as CASSCF), which gives a proper description of the major features in the electronic structure of the excited state, independent of its complexity, accounts for all near degeneracy effects, and includes full orbital relaxation.The remaining dynamic electron correlation effects are in a subsequent step added using second-order perturbation theory with the CASSCF wave function as the reference state. The approach is tested here in a calculation of the valence excited singlet states of the azabenzenes pyridine, pyrazine, pyrimidine, pyridazine, and s-triazine, using a (C,N,4~3pZd/H,3s2p) atomic natural orbital (ANO) basis. The ?M* excitation energies of the azabenzenes are computed with an average error of 0.14 eV. With the exception of one case, the n-r* excitation energies are computed with an accuracy of 0.32 eV or better in all cases where a comparison with reliable experimental data can be made.

The electric field gradient (EFG) tensors for Al and O atoms in corundum and for C and D(ZH) in hexadeuterobenzene (C6D6) are determined from accurate X-ray diffraction data using four independent computational strategies. Two of the strategies capitalize on the fact that the electric field gradient is the second derivative of the electrostatic potential, a simple relationship which has not been exploited previously in analyses of diffraction data. The convergence behaviour of the tensor components calculated by each strategy is examined for both systems, and the fully converged results obtained with each computational strategy are shown to be identical. It is found that the orientation of the tensors and the signs of their components are well determined from diffraction data, but the magnitudes and asymmetry of the components are not. Discrepancies in previous analyses of the corundum data are resolved, and it is shown that the origin of the EFG at hydrogen is quite different from that at heavier nuclei. Successful determination of EFGs from X-ray diffraction data appears within reach, but will require precise knowledge of atomic position and thermal parameters, more extensive data sets than are currently available, and a more flexible pseudoatom model than presently used.

The electron density distribution in H2S2, S2, S3, S4, S6, S8, 2,5-dimethyl-6a-thiathiophthene (DMT), tetramethylthiuram disulfide (TMTD), and S4N4 are examined using ab initio linear combination atomic orbital–molecular orbital methods. The inclusion of polarization functions in the basis set is found to be necessary to give a satisfactory description of the electron density distribution in these molecules. The effects of electron correlation on the electron density distribution in H2S2, S2, and S3 are assessed using configuration interaction, and are found to be less important than the use of polarization functions in the basis set. Comparisons of theoretical and experimental electron density distribution maps are made for S8, DMT, TMTD, and S4N4. The deformation density in sulfur–sulfur bonds is found to have a single peak at the bond midpoint, in contrast to the complicated double-maximum distribution commonly observed in experimental studies. The presence of deformation density peaks between across-the-ring sulfur atoms in S4N4 is confirmed, but a peak at the center of the molecule is not.