Arbitrary configuration interaction

The UHF option allows only the lowest state of a given multiplicity to be requested. Thus, for example, you could explore the lowest Triplet excited state of benzene with the UHF option, but could not ask for calculations on an excited singlet state. This is because the UHF option in HyperChem does not allow arbitrary orbital occupations (possibly leading to an excited single determinant of different spatial symmetry than the lowest determinant of the same multiplicity), nor does it perform a Configuration Interaction (Cl) calculation that allows a multitude of states to be described. 

The electron correlation problem remains a central research area for quantum chemists, as its solution would provide the exact energies for arbitrary systems. Today there exist many procedures for calculating the electron correlation energy (/), none of which, unfortunately, is both robust and computationally inexpensive. Configuration interaction (Cl) methods provide a conceptually simple route to correlation energies and a full Cl calculation will provide exact energies but only at prohibitive computational cost as it scales factorially with the number of basis functions, N. Truncated Cl methods such as CISD (A cost) are more computationally feasible but can still only be used for small systems and are neither size consistent nor size extensive. Coupled cluster... 

In principle, the theory reviewed in Sections 4-6 can be applied to interactions of arbitrary systems if the full configuration interaction (FCI) wave functions of the monomers are available, and if the matrix elements of H0 and V can be constructed in the space spanned by the products of the configuration state functions of the monomers. For the interactions of many-electron monomers the resulting perturbation equations are difficult to solve, however. A many-electron version of SAPT, which systematically treat the intramonomer correlation effects, offers a solution to this problem. 

The vibration-rotation interaction is the effect arising from coupling terms between angular and vibrational momenta as well as from the dependence of the rotational G-matrix elements (the /u-tensor) on the internal coordinates. The importance of this effect may to some extent be reduced provided an appropriate axis convention is used. The axis convention is the set of rules defining the orientation of the molecular axes, eg, g = x,y, z, relative to an arbitrary configuration as given by the position vectors, Ra, a. = 1, 2,... N. These rules can be expressed in three relations between the rag components, similar to the center of mass conditions(2.4). We shall refer to these relations as the axial constraints . Usually Eckart-condi-tions39 are imposed, but other possibilities may be considered. 

The first thing we must do is select a particular orbit. This is done by choosing an initial wavefunction, as the choice of the initial wavefunction determines the orbit. Consider, for example, an arbitrary wavefunction M e cty. This can be a configuration interaction wavefunction or some trial wavefunction incorporating inter-particle coordinates. These wavefunctions must allow for a proper representation of the important physical aspects of the problem at hand. Thus, a configuration interaction wavefunction should contain the minimal set of configurations necessary for the description of electronic correlation. 

In the non-variational procedure, one sets up an arbitrary orbit-generating wave-function whose form is designed so as to contain the physics" of the problem under consideration. If one were to choose a configuration interaction wavefunction, it... 

Let us consider an interacting adsorbed layer which consists of three distinct species activated complexes of arbitrary configuration (total number of different kind of complexes = M,) multi-centred adsorbed species (total number of different types Mm) uni-centred adsorbed species (total number = Mh). The partition function for the adsorbed layer is given by... 

An alternative CNDO procedure for Cl, developed at the same time as CNDO/S but oriented toward ground-state properties is the PCILO (perturbative configuration interaction using localized orbitals) method of Malrieu, Claverie, Diner, and co-workers. °" Its major strength and weakness lie in the use of intuitively construaed hybrid atomic orbitals as zeroeth-order localized MOs. This leads to conceptually appealing interpretations at the expense of some arbitrariness in the treatment. 

The explicit time-dependent configuration interaction (TD-CI) method has been applied to calculate the linear and nonlinear electric responses of H2 and H2O molecules to external time-dependent perturbations. Three variants have been employed to solve the time-dependent Schrodinger equation, namely, the TD-CIS (inclusion of single excitations only), TD-CISD (inclusion of single and double excitations), and TD-CIS(D) (single excitations and a perturbative treatment of the double excitations) methods. The authors have stressed that one of the biggest advantages of this approach is its ability to tackle molecular responses to pulses with arbitrary time-dependence, even beyond perturbation theory. 

In order to calculate the spin-angular parts of matrix elements of the two-particle operator (1) with an arbitrary number of open shells, it is necessary to consider all possible distributions of shells upon which the second quantization operators are acting. In [2] they are found to be grouped into 42 different distributions, subdivided into 4 different classes. This also explains why operator (1) is written as the sum of four complex terms. The first term represents the case when all second-quantization operators act upon the same shell (distribution 1 in [2]), the second describes the situation when these operators act upon the two different shells (distributions 2-10), third and fourth are in charge of the interactions upon three and four shells respectively (distributions 11-18 and 19-42). Such expression is particularly convenient to take into account correlation effects, because it describes all possible superpositions of configurations for the case of two-electron operator. 

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