Symmetrically orthogonalized overlap

Results obtained from the alkali iodides on the isomer shift, the NMR chemical shift and its pressure dependence, and dynamic quadrupole coupling are compared. These results are discussed in terms of shielding by the 5p electrons and of Lbwdins technique of symmetrical orthogonalization which takes into account the distortion of the free ion functions by overlap. The recoilless fractions for all the alkali iodides are approximately constant at 80°K. Recent results include hybridization effects inferred from the isomer shifts of the iodates and the periodates, magnetic and electric quadrupole hyperfine splittings, and results obtained from molecular iodine and other iodine compounds. The properties of the 57.6-k.e.v. transition of 1 and the 27.7-k.e.v. transition of 1 are compared. 

Chirgwin- Coulson Inverse- overlap Symmetric orthogon. EGSO ... 

SINDO symmetrically orthogonalized intermediate neglect of differential overlap... 

Now, if the differential overlaps of the original AO basis are approximated by the formula eq. (2.28), it turns out that applying the Lowdin transformation S 2 to the set of the AOs makes the products i.e. the differential overlaps of the symmetrically orthogonal OAOs vanishing ... 

CNDO/S, CNDO/FK, CNDO/BW, INDO/1, INDO/2, INDO/S and SINDOl. These methods are rarely used in modem computational chemistry, mainly because the modified methods described below usually perform better. Exceptions are INDO based methods, such as SlNDOl and INDO/S. SINDO Symmetric orthogonalized INDO) employes the INDO approximations described above, but not the ZDO approximation for the overlap matrix. The INDO/S method (INDO parameterized for Spectmscopy) is especially designed for calculating electronic spectra of large molecules or systems involving heavy atoms. 

ZDO schemes are often rationalized on the basis of a symmetrical orthogonalization of an overlapping basis.The scheme most often used is... 

U. As U is neither normalized nor orthogonal, we introduce an overlap matrix S defined in Equation 15 and use Lowdin s symmetric orthogonalization scheme to... 

A symmetrical orthogonalization corresponds to a transformation that has the property X SX = I, where X denotes all the x, coordinate vectors and S contains the overlap elements. One such transformation is given by the inverse square root of the overlap matrix (X = ), a procedure used in solving the self-consistent field equations in... 

S is an overlap matrix. The eigenvalue problem is evaluated by symmetric orthogonalization. 

Semiempirical SCF calculations were done using the approximations NDDO (neglect of diatomic differential overlap) [18], MNDO (modified neglect of diatomic overlap) [19], INDO (intermediate neglect of differential overlap) [20], SINDO (symmetrically orthogonalized INDO [21]) [22], and CNDO (complete neglect of differential overlap) [20, 23]. Another type of approximation [24] to the ab initio method was also applied to OF2 [16]. 

All the various options influence the result of a population analysis. However, before a final assessment can be made we must address the more basic problem of a category for the population analysis. The most popular analysis is the Mulliken analysis for nonorthogonal AOs and equal partitioning of overlap between the two atoms involved. If the ZDO assumption is maintained for the Fock matrix eigenvalue problem, an orthogonalized AO basis must be considered. In such semiempirical methods the symmetric orthogonalization is most frequently implied. 

MNDO = modified neglect of diatomic overlap MNDO/d = modified neglect of diatomic overlap with d-type orbitals NLDF = nonlocal density functional PM3/d = parametric method three with d-type orbitals SINDOl = symmetrically orthogonalized intermediate neglect of diatomic overlap parametrization one TM = transition metal UFF = universal force field ZINDO = Zemer s intermediate neglect of diatomic overlap. 

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