Virtual space

Our results fit also with a previous investigation (9) on polyenes based on a version of the 2h-lp Cl scheme restricted to the virtual one-electron states generated by a minimal basis. In our case, however, the fragmentation of lines into satellites is much more pronounced. The reason lies in the size-consistency of the ADC[3] approach (as contrasted with the size-inconsistency of any truncated form of Cl (27d), in the full handling of the virtual space, and (10) in the inclusion of correlation corrections to the reference ground state, leading to (37) a net reduction of the quasi-particle band gap of conjugated polymers. 

All three states were described by a single set of SCF molecular orbitals based on the occupied canonical orbitals of the X Z- state and a transformation of the canonical virtual space known as "K-orbitals" [10] which, among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical intemuclear distances, i.e. R. (equilibrium geometry) and about 3Re,and adding to the HF... 

In principle, the deficiencies of HF theory can be overcome by so-called correlated wavefunction or post-HF methods. In the majority of the available methods, the wavefunction is expanded in terms of many Slater-determinants instead of just one. One systematic recipe to choose such determinants is to perform single-, double-, triple-, etc. substitutions of occupied HF orbitals by virtual orbitals. Pictorially speaking, the electron correlation is implemented in this way by allowing the electrons to jump out of the HF sea into the virtual space in order... 

Comparison with experimental values are meaningful only for boron and aluminum. The MRCI values for AI (0.45 eV) and the MCDF results for B (0.26 eV) and A1 (0.43 eV) are in good agreement with the Hotop and Lineberger values (0.28 and 0.44 eV, respectively). The MRCI and MCDF EAs for the other atoms agree with each other (0.29 and 0.30 eV for Ga, 0.38 and 0.39 eV for In, 0.27 and 0.29 eV for Tl). The RCC EA of TI is much higher at 0.40(5) eV. A major difference between the RCC and the other two methods lies in the number of electrons correlated. While [52] and [53] correlate valence electrons only, three for the neutral atom and four for the anion, we correlated 35 electrons in Tl and 36 in TE. A RCC study of all five elements was undertaken [54], with the aim of determining all five EAs and, in particular, the effect of inner-shell correlation and virtual space used on the calculated values. 

Multireference There is no division into occupied and virtual orbitals, all orbitals appear on an equal footing in the ansatz (Equation 8). In particular, the Hartree-Fock reference has no special significance here. For this reason, we expect (and observe) the ansatz to be very well balanced for describing nondynamic correlation in multireference problems (see e.g., refs. 10-12). Conversely, the ansatz is inefficient for describing dynamic correlation, since to treat dynamic correlation one would benefit from the knowledge of which orbitals are in the occupied and virtual spaces. 

The global basis x used in the calculations rejKuted here is again of simple contracted gaussian form it contains four contracted s functions and three sets of contracted p functions on the chlorine atom three contracted s functions and two sets of contracted p functions on the lithium. When the orbitals are written in the matrix form 4> = xT, the first 8 columns of T, namely Toor, define the doubly occupied core orbitals the 3 columns of Tv i define the sigma lone p>air and the two orbitals of the bond pair and the 11 columns of Toom provide the complementary (virtual) space. 

In the publications from the Tripos group, the authors had demonstrated that they could bypass the need for full enumeration of a huge virtual space and enable similarity search by extensively leveraging the reactant-level information (10). Even though... 

Finally we hope to see that more validation studies are conducted to compare any new search method with the reference exhaustive search (of course on a smaller validation virtual space of 104-106). Only through this type of rigorous validation studies, one can truly probe the rates of false positives and false negatives as well as the fold increase in search speed. This in turn allows end users to make informed decisions on which search method will be a best match for their specific tasks. 

Peng, Z., et al. PGVL a vast virtual space of synthetic feasible compounds based on... 

Electron density difference matrices that correspond to the transition energies in the EP2 approximation may be used to obtain a virtual orbital space of reduced rank [27] that introduces only minor deviations with respect to results produced with the full, original set of virtual orbitals. This quasiparticle virtual orbital selection (QVOS) process provides an improved choice of a reduced virtual space for a given EADE and can be used to speed up computations with higher order approximations, such as P3 or OVGF. Numerical tests show the superior accuracy and efficiency of this approach compared to the usual practice of omission of virtual orbitals with the highest energies [27],... 

Table 1.7 shows quasi-particle calculations with a virtual space whose dimension has been reduced by the use of the QVOS procedure. As much as 50% of the virtual space s dimension was eliminated in these calculations, and errors of only 0.1 eV were introduced. With the larger, cc-pVQZ basis set, the errors that are introduced are smaller. In general, a larger basis set will result in a larger virtual space, and therefore, a larger reduction (in percentages) is possible. In P3 calculations on the larger molecules, benzene and borazine, similar errors were found [27],... 

An interesting development that can be used by companies to answer some of their R D problems, involves the use of internet sites for forums designed to be virtual knowledge bases, for example InnoCentive. On this website companies can anonymously describe their scientific problems so that they can be solved by outsiders. Over 50,000 scientists have registered with InnoCentive so there is an excellent chance that someone has an answer out there in virtual space. The person who successfully answers the problem gets a not insignificant cash prize from the seeker company [B-41]. Several major companies such as Procter Gamble and Henkel say they have benefited from the use of InnoCentive [B-42]. 

In electron correlation treatments, it is a common procedure to divide the orbital space into various subspaces orbitals with large binding energy (core), occupied orbitals with low-binding energy (valence), and unoccupied orbitals (virtual). One of the reasons for this subdivision is the possibility to freeze the core (i.e., to restrict excitations to the valence and virtual spaces). Consequently, all determinants in a configuration interaction (Cl) expansion share a set of frozen-core orbitals. For this approximation to be valid, one has to assume that excitation energies are not affected by correlation contributions of the inner shells. It is then sufficient to describe the interaction between core and valence electrons by some kind of mean-field expression. 

The accuracy of the MO-VB wavefunction is expected to be close to that of a full SD-CI wavefunction involving excitations to the full virtual spaces of each monomer (vertical excitations). Very recently, a new version of the MO-VB optimization scheme has been developed that is apt to guarantee that the wavefunction approaches as close as possible the full SD-CI limit, via saturation of the optimal virtual space. Explorative calculations on the very challenging helium dimer system are encouraging. 

Extension of the MO-VB scheme saturation of the optimal virtual space... 

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