Full CI calculation

Thus, full CI calculations with large basis sets are usually carried out for only the smallest of molecules (it is partly as a result of such calculations that the relative contributions to basis-set quality of polarization functions vs. decontraction of valence functions, as discussed in Chapter 6, were discovered). In larger systems, the practical restriction to smaller basis sets makes full CI calculations less chemically interesting, but such calculations remain useful to the extent that, as an optimal limit, they permit an evaluation of the quality of other methodologies for including electron correlation using the same basis set. We turn now to a consideration of such other methods. 

As in Sect.6.1, comparison with SCF and full-CI curves (the latter, even with frozen Is cores, involving almost 10 million Slater determinants), testifies to the adequacy of the description in terms of three VB structures, the reduced energy curve being in excellent agreement with that from the full-CI calculation. 

Bendazzoli, G.L., Magnasco, V., Figari, G., and Rui, M. (2000) Full-CI calculation of imaginary frequency-dependent dipole polarizabilities of ground state LiH and the Cg dispersion coefficients of LiH-LiH. Chem. Phys. Lett., 330, 146-151. 

With these data a LFDFT full-CI calculation yields D ( A2) = 26cm in agreement with the experimental value (29 cm [81]). As follows from Equation 31-33, the largest contribution to D (80%) results from the mixing of the A2 ground term with the nearest Aj state. 

The convergence of the calculated HFSCs with respect to the order of / -operators was also examined [142]. In Fig. 39.24, the HFSCs calculated by the SAC-CI SD-R and general-/ methods are compared with the full-CI values. The calculations are due to the double-zeta basis sets because of the limitation of the full-CI calculations. The SAC-CI values almost converge to the full-CI values when the / -operators are included up to... 

Full-CI calculations using the MELDF system of programs [26] yielded the surfaces shown in Figure 7. The X-axis represents the distance from the Be atom to the H2 moiety, while the Y-axis represents the distance between the two hydrogen atoms. Of the two surfaces, the one above is repulsive and has a deep valley at Y 2.0 a.u. A similar valley exists on the lower surface as well, with a clear minimum at X=3.0 a.u and Y=1.52 a.u. The Full Cl energy at the minimum was determined to be -14.8563 a.u. 

It is instructive to consider a very simple system for which, using a limited basis, a direct comparison of perturbation and full-CI calculations is possible. The Cl approach is finite and leads at once to the basis-set limit, but the perturbation theory rests upon the expansions (9.4.7) and (9.4.8), which are infinite series in powers of a perturbation parameter and may or may not converge to the same limit. 

For /2(Ar)i7, an extensive CI-CSP simulation was carried out, and the results were compared with those of the simple CSP approximation. Both calculations are for the ultrafast dynamics following excitation of the I2 into the B state. We found that the CI-CSP calculation, including doubly excited configurations , is close to converged for times up to t 500 fs, when 1500 configurations are included. Fig. 2 shows co(t)p, the coefficient of the CSP term and the doubly excited terms in the full CI-CSP wavefunction,... 

In our first ONIOM study, we showed the advantages of combining two molecular orbital (MO) methods in calculations of the chromophore itself. Compared to a full CASSCF treatment of a scaled chromophore (PSBN in Figure 2-3), a two-layer ONIOM (CASSCF CIS) calculation where only parts of the conjugated system (PSBN8 in Figure 2-3) is included in the model system, reproduces the... 

Next, SDTQ-CI calculations are performed for a few truncated quadruple expansions with quadruple truncation degrees in the expected range (around 10% of all quadruple space products). Furthermore, using our estimation formula (2.6), the quadruple normalization deficiencies of these wavefimctions relative to the full SDTQ wavefiinction are readily estimated as... 

As shown in Table 2, the inexpensive MMCC(2,3)/CI approach is capable of providing the results of full EOMCCSDT quality. Indeed, the errors in the vertical excitation energies for the 2 S+, 1 A, 2 A, and 2 states of CH+ that have large double excitation components, obtained with the noniterative MMCC(2,3)/CI approximation, are 0.006-0.105 eV. This should be compared to the 0.327-0.924 eV errors in the EOMCCSD results, the 0.219-0.318 eV errors obtained with the CC3 method, and the 0.504-0.882 eV errors obtained with the CISDt approach used to construct wave functions T ) for the MMCC(2,3)/CI calculations [47,48]. For the remaining states shown in Table 2 (the third and fourth states and the lowest-energy state), the errors in the CISDt-corrected MMCC(2,3) results, relative to full Cl, are 0.000-0.015 eV. Again, the only standard EOMCC method that can compete with the MMCC(2,3)/CI approach is the expensive full EOMCCSDT approximation. 

Having discussed ways to reduce the scope of the MCSCF problem, it is appropriate to consider the other limiting case. What if we carry out a CASSCF calculation for all electrons including all orbitals in the complete active space Such a calculation is called full configuration interaction or full CF. Witliin the choice of basis set, it is the best possible calculation that can be done, because it considers the contribution of every possible CSF. Thus, a full CI with an infinite basis set is an exact solution of the (non-relativistic, Bom-Oppenheimer, time-independent) Schrodinger equation. 

If we consider all possible excited configurations that can be generated from the HF determinant, we have a full CI, but such a calculation is typically too demanding to accomplish. However, just as we reduced the scope of CAS calculations by using RAS spaces, what if we were to reduce the CI problem by allowing only a limited number of excitations How many should we include To proceed in evaluating this question, it is helpful to rewrite Eq. (7.1) using a more descriptive notation, i.e.. 

The CD induced in 2-(2,4,6-cycloheptatrien-l-ylidine)-4-cyclopentene-l,3-dione upon its inclusion in 6-cyclodextrin was used to obtain full assignment of the observed absorption bands [49]. It was concluded that the low energy band system was composed of three electronic transitions, two of which were polarized perpendicular, and one parallel, with respect to the long molecular axis of the solute. The higher energy band system was found to also consist of three allowed electronic transitions, but two of these were polarized parallel, and one perpendicular, to the long axis of the solute molecule. These deductions were supported by a series of CNDO/S-CI calculations performed on the system. A similar approach was taken to assign the polarizations of the various transitions associated with 2-thioxo-l,3-benzodithiole and 2-selenoxo-1,3-benzodithiole [50]. 

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