Guess, initial

A configuration interaction calculation uses molecular orbitals that have been optimized typically with a Hartree-Fock (FIF) calculation. Generalized valence bond (GVB) and multi-configuration self-consistent field (MCSCF) calculations can also be used as a starting point for a configuration interaction calculation. 

The extended CIS method (XCIS) is a version of CIS for examining states that are doubly excited from the reference state. It does not include correlation and is thus similar in accuracy to CIS. 

The CIS(D) method is designed to include some correlation in excited states. Initial results with this method show that it is stable and reliable and gives excitation energies significantly more accurate than those of CIS. 

---

An initial guess for the reactor conversion is very difficult to make. A high conversion increases the concentration of monoethanolamine and increases the rates of the secondary reactions. As we shall see later, a low conversion has the effect of decreasing the reactor capital cost but increasing the capital cost of many other items of equipment in the flowsheet. Thus an initial value of 50 percent conversion is probably as good as a guess as can be made at this stage. 

To make an initial guess for the reactor conversion is again diflicult. The series nature of the byproduct reactions suggests that a value of 50 percent is probably as good as csm be suggested at this stage. 

Start with an initial guess for DCFRR of 20 percent and increase ... 

Despite the complexity of these expressions, it is possible to hrvert transport coefficients to obtain infomiation about the mtemiolecular potential by an iterative procedure [111] that converges rapidly, provided that the initial guess for V(r) has the right well depth. 

After the requisite integrals are available or are being computed on the fly, to begin the SCE process one must input into the computer routine which computes F the initial guesses for the C. values corresponding to... 

Once the initial guesses have been made for the. of the occupied orbitals, the Ilill matrix is fonued and new e. and. values are obtained by solving. . These new orbitals are tlien... 

As Bartlett [ ] and Pople have both demonstrated [M], there is a close relationship between the MPPT/MBPT and CC methods when the CC equations are solved iteratively starting with such an MPPT/MBPT-like initial guess for these double-excitation amplitudes. 

Some initial guess is made for the LCAO-KS expansion coefficients C. a a... 

To compute the above expression, short molecular dynamics runs (with a small time step) are calculated and serve as exact trajectories. Using the exact trajectory as an initial guess for path optimization (with a large time step) we optimize a discrete Onsager-Machlup path. The variation of the action with respect to the optimal trajectory is computed and used in the above formula. 

Projected CNDO ihe initial guess at the MCi coefficients is obtained from a CNDO calculation ... 

However, th ese alternative methods can be on ly applied to certain elements. For example, the projected CXDO/IXDOi may be used only for molecular system s with atom ic n iiin bers less than or ct nal to IS (Ari. Elements beyond IS are not available in the projected CXDO/IXD(f initial guess. 

Living calculated the integrals, we are now ready to start the SCF calculation. To formulate the Fock mahix it is necessary to have an initial guess of the density matrix, P. The simplest approach is to use the null matrix in which all elements are zero. In this initial step the Fock nulrix F is therefore equal to... 

To. solve the Kohn-Sham equations a self-consistent approach is taken. An initial guess of the density is fed into Equation (3.47) from which a set of orbitals can be derived, leading to an improved value for the density, which is then used in the second iteration, and so on until convergence is achieved. 

To avoid imposition of unrealistic exit boundary conditions in flow models Taylor et al. (1985) developed a method called traction boundary conditions . In this method starting from an initial guess, outflow condition is updated in an iterative procedure which ensures its consistency with the flow regime immediately upstream. This method is successfully applied to solve a number of turbulent flow problems. 

Several questions present themselves immediately How good does the initial guess have to be How do we know that the procedure leads to better guesses, not worse How many steps (how long) will the procedure take How do we know when to stop These questions and others like them will play an important role in this book. You will not be surprised to leam that answers to questions like these vary from one problem to another and cannot be set down once and for all. Let us start with a famous problem in quantum mechanics blackbody radiation. 

Fj V initial guesses for the Cy i values eorresponding to the oeeupied orbitals. These... 

Fjj,v Cy i 8i Zy Sjj y Cy j as initial guesses for the Cy i. Using only the one-eleetron part of the Hamiltonian to determine initial values for the LCAO-MO eoeffieients may seem like a rather severe step it is, and the resultant Cy i values are usually far from the eonverged values whieh the SCF proeess eventually produees. However, the initial Cy i obtained in this manner have proper symmetries and nodal patterns beeause the one-eleetron part of the Hamiltonian has the same symmetry as the full Hamiltonian. 

---