SCF Iteration

The iteration may require a number of special techniques to achieve convergence and may take anywhere from 10 to 100 iterations depending on the convergence technique and the initial gness. Upon electronic convergence the nuclear repulsion energy is added to the total. 

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Pulay P 1980 Convergence acceleration in iterative sequences the case of SCF iteration Chem. Phys. Lett. 73 393... 

The calculation proceeds as illustrated in Table 2.2, which shows the variation in the coefficients of the atomic orbitals in the lowest-energy wavefunction and the energy for the first four SCF iterations. The energy is converged to six decimal places after six iterations and the charge density matrix after nine iterations. 

Give the calculation (with DIIS) more SCF iterations. This seldom helps, but the next option often uses so many iterations that it is worth a tiy. 

Convergence limit and Iteration limit specify the precision of the SCF calculation. Con vergen ce lim it refers to th e difference in total electronic energy (in kcal/mol) between two successive SCF iterations yielding a converged result. Iteration limit specifies the maximum number of iterations allowed to reach that goal. 

Set this threshold to a small positive constant (the default value is 10" ° Hartree). This threshold is used by HyperChem to ignore all two-electron repulsion integrals with an absolute value less than this value. This option controls the performance of the SCF iterations and the accuracy of the wave function and energies since it can decrease the number of calculated two-electron integrals. 

SCF procedure is begun, and then used in each SCF iteration. Formally, in the large basis set limit the SCF procedure involves a computational effort which increases as the number of basis functions to the fourth power. Below it will be shown that the scaling may be substantially smaller in acmal calculations. 

There are two ways of handling the interaction between the QM region and MM region one way is to calculate electrostatic QM-MM interaction with the MM method (sometimes called mechanical embedding, or ME) and the other is to include the QM-MM interaction in the QM Hamiltonian (called electronic embedding or EE). The major difference is that in the ME scheme the QM wave function is the same in the gas phase and the electrostatic interaction is included classically, while in the EE scheme the QM wave function is polarized by the MM charges. The EE scheme is substantially more expensive than ME scheme, as the SCF iteration needs to be performed until self-consistency is achieved for QM electron distribution. Although the polarization effects are called important, as we will show later,... 

In order to circumvent this problem, one may either manipulate the initial guess or set up a constrained optimization, where the SCF iterations converge to predefined (constrained) properties. The latter was achieved in a protocol by Van Voorhis and coworkers (133-135). This approach suffers from the fact that the constrained Slater determinant may not represent a local energy minimum of the unconstrained potential energy surface. 

The advantage of such an optimization scheme is that the SCF iterations do not converge to a non-stationary energy on the unconstrained potential energy surface that may only represent an energy minimum on the constrained potential energy surface, but to a true energy minimum, where the final local spin values—within a certain threshold—may differ from the ideal ones. 

In Eq. (1-6), E) , vcnt refers to the total solvent electric field and it contains a sum of contributions from the point charges and the induced dipole moments in the MM part of the system. Such a field (and hence the induced dipole) depends on all other induced dipole moments in the solvent. This means that Eq. (1-6) must be solved iteratively within each SCF iteration. As an alternative, Eq. (1-6) may be reformulated into a matrix equation... 

An interesting alternative to van der Waals cavities is the use of isodensity or isopotential surfaces. Rivail et al. [70] demonstrated that for a given cavity volume, the electron isopotential surface is the one containing the largest electronic density, thus giving a physical meaning to this surface. Nevertheless, isodensity and isopotential cavities are computationally demanding, as they have to be recomputed at each SCF iteration, and are not quite used in practice. 

Accordingly, the modifications to the KS operator are twofold (i) a static contribution through the static multipole moments (here charges) of the solvent molecules and (ii) a dynamical contribution which depends linearly on the electronic polarizability of the environment and also depends on the electronic density of the QM region. Due to the latter fact we need within each SCF iteration to update the DFT/MM part of the KS operator with the set of induced dipole moments determined from Eq. (13-29). We emphasize that it is the dynamical contribution that gives rise to polarization of the MM subsystem by the QM subsystem. 

The numerical atomic orbital generated by solving the Schrodinger equation for "atom in molecule" is employed as a basis function of LCAO, which is renewed for each SCF iteration taking a modification of charge density into account. The atomic orbitals up to nd, (n+l)s and n+l)p are utilized for nd transition elements, where n is 3,4 and 5. The MO energy and the wave function are obtained by solving the secular equation. 

TUtegrals was the only option. Modem machines often have quite significant amounts off memory, a few Gbytes is not uncommon. For small and medium sized systems it may be possible to store all the integrals in the memory instead of on disk. Such in-core methods are very efficient for performing an HF calculation. The integrals are only calculated once, and each SCF iteration is just a multiplication of the integral tensor... 

In the present DV-Xa method, the numerical atomic orbitals are utilized to construct the basis set, different from the other MO methods. The wave function is obtained by numerically solving Schrodinger equation for " atom in molecule". The effective charge of the atom in molecule varies every SCF iteration until it converges at the SCF. Then, the atomic orbitals are computed at each iteration in order to supply the optimal basis functions for the molecular... 

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