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AO basis

The oharge- and exohange-density matrix elements in the AO basis are ... [Pg.2169]

The fundamental core and valence basis. In constructing an AO basis, one can choose from among several classes of fiinctions. First, the size and nature of the primary core and valence basis must be specified. Within this category, the following choices are connnon. [Pg.2171]

Once one has specified an AO basis for each atom in the molecule, the LCAO-MO procedure can be used to... [Pg.2172]

An AO basis is chosen in tenns of which the KS orbitals are to be expanded. [Pg.2183]

The density is computed as p(r) = 2. n i ). (/ )p. Often, p(r) is expanded in an AO basis, which need not be the same as the basis used for the and the expansion coefficients of p are computed in tenns of those of the It is also connnon to use an AO basis to expand p (r) which, together with p, is needed to evaluate the exchange-correlation fiinctionaTs contribution toCg. [Pg.2183]

Essentially all of the teclmiques discussed above require the evaluation of one- and two-electron integrals over the AO basis fiinctions (x l./lx ) and mentioned earlier, there are of the order of A /8... [Pg.2185]

For all calculations, the choice of AO basis set must be made carefully, keeping in mind the scaling of the two-electron integral evaluation step and the scaling of the two-electron integral transfonuation step. Of course, basis fiinctions that describe the essence of the states to be studied are essential (e.g. Rydberg or anion states require diffuse functions and strained rings require polarization fiinctions). [Pg.2189]

Density matrix element in AO basis Matrix eigenvalue van der Waals parameter Dielectric constant... [Pg.403]

Extended Hiickel calculations are performed with a nonorthogonalized AO basis set therefore, the spin densities are to be evaluated by gross atomic populations and not simply by squares of expansion coefficients. [Pg.349]

The analytical determination of the derivative dEtotldrir of the total energy Etot with respect to population n, of the r-th molecular orbital is a very complicated task in the case of methods like the BMV one for three reasons (a), those methods assume that the atomic orbital (AO) basis is non-orthogonal (b), they involve nonlinear expressions in the AO populations (c) the latter may have to be determined as Mulliken or Lbwdin population, if they must have a physical significance [6]. The rest of this paper is devoted to the presentation of that derivation on a scheme having the essential features of the BMV scheme, but simplified to keep control of the relation between the symbols introduced and their physical significance. Before devoting ourselves to that derivation, however, we with to mention the reason why the MO occupation should be treated in certain problems as a continuous variable. [Pg.119]

The results of the above cited applications [18-28,45] have clearly shown that CS INDO method is fairly successful in combining equally satisfactory predictions of electronic spectra and potential surfaces (especially along internal rotation pathways) of conjugated molecules, a goal never reached by other NDO-type procedures. CS INDO shares, at least partly, the interpretative advantages of the CIPSI-PCILO-CNDO procedure [32,33,36,37], coming from using the same hybrid AO basis sets, but improves its predictive capabilities as far as spectroscopic and photochemical properties are concerned. [Pg.383]

With reference to the individual AO basis sets

fragment density matrices P t((p (Kt)) obtained from parent molecules Ms of nuclear configurations Kt, on the one hand, and the macromolecular AO basis set cp (K) of the macromolecular density matrix P (cp (K)) associated with the macromolecular nuclear configuration K, on the other hand, the following mutual compatibility conditions are assumed ... [Pg.71]

In fact, for a simple, but still remarkably usefi.il first approximation of the electronic density of the new nuclear arrangement K k. one may use the same density matrix Pk ((pKi.)), but in combination with a new basis set cp (K t) obtained by simply moving the centers of the old AO basis functions to the new nuclear locations,... [Pg.74]

The formal vector cp (K) denotes the set of atomic orbital basis functions with centers at the original nuclear locations of the macromolecular nuclear configuration K, where the components cp(r, K) of vector q(K) are the individual AO basis functions. The macromolecular overlap matrix corresponding to this set cp (K) of AO s is denoted by S(K). The new macromolecular basis set obtained by moving the appropriate local basis functions to be centered at the new nuclear locations is denoted by cfcK ), where the notation cp(r, K ) is used for the individual components of this new basis set overlap matrix is denoted by S(K ). [Pg.74]

Except for the initial AO —NAO transformation, which starts from non-orthogonal AOs, each step in (3.38) is a unitary transformation from one complete orthonormal set to another. Each localized set gives an exact matrix representation of any property or function that can be described by the original AO basis. [Pg.115]

In order to contrast the MO-type and VB-type descriptions, we may say that the former attempts to describe the MOs (or NOs) in terms of general mixings of AO basis functions (LCAO-MO description),... [Pg.566]

Figure 4.105 A schematic perturbative-analysis diagram for occupied valence MOs (center) of PtH42 (B3LYP/LANL2DZ level), showing tie-lines for analysis in terms of AO basis functions (left) versus NAOs (right). (A tie-line is shown when the AO or NAO contributes at least 5% to the connected MO.) Note the much smaller number of contributing orbitals, the sparser tie-line patterns, and the more realistic physical range of atomic orbital energies for NAOs than for standard Gaussian-basis AOs. Figure 4.105 A schematic perturbative-analysis diagram for occupied valence MOs (center) of PtH42 (B3LYP/LANL2DZ level), showing tie-lines for analysis in terms of AO basis functions (left) versus NAOs (right). (A tie-line is shown when the AO or NAO contributes at least 5% to the connected MO.) Note the much smaller number of contributing orbitals, the sparser tie-line patterns, and the more realistic physical range of atomic orbital energies for NAOs than for standard Gaussian-basis AOs.
We see therefore that, however desirable it is to abandon symmetry constraints from the point of view of the variation method, we shall be involved in radical departures from the conventional AO expansion method - particularly in its minimal basis form. Indeed most of the changes required to the usual AO basis method are already implicit in any decision to lower the symmetry of the AO basis from its local spherically symmetric form to that of the molecular point group. We shall see later that these considerations are too pessimistic. [Pg.48]


See other pages where AO basis is mentioned: [Pg.2161]    [Pg.2169]    [Pg.2170]    [Pg.2174]    [Pg.2184]    [Pg.2188]    [Pg.2189]    [Pg.173]    [Pg.464]    [Pg.247]    [Pg.403]    [Pg.403]    [Pg.405]    [Pg.361]    [Pg.371]    [Pg.125]    [Pg.381]    [Pg.71]    [Pg.71]    [Pg.72]    [Pg.72]    [Pg.73]    [Pg.75]    [Pg.176]    [Pg.18]    [Pg.18]    [Pg.33]    [Pg.74]    [Pg.566]    [Pg.567]    [Pg.150]    [Pg.40]   


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AO basis sets

Implementations of AO basis sets

The AO basis

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