Configuration-interaction theory representation

Fig. 11.6 shows the noncoplanar-symmetric differential cross sections at 1200 eV for the Is state and the unresolved n=2 states, normalised to theory for the low-momentum Is points. Here the structure amplitude is calculated from the overlap of a converged configuration-interaction representation of helium (McCarthy and Mitroy, 1986) with the observed helium ion state. The distorted-wave impulse approximation describes the Is momentum profile accurately. The summed n=2 profile does not have the shape expected on the basis of the weak-coupling approximation (long-dashed curve). Its shape and magnitude are given quite well by... 

To obtain errors of 1 kcal/mol or better, it is essential to treat many-body effects accurately and, we believe, directly. Although commonly used methods such as the density functional theory within the local density approximation (LDA) or the generalized gradient approximation (GGA) may get some properties correctly, it seems unlikely that they, in general, will ever have the needed precision and robustness on a wide variety of molecules. On the other hand, methods that rely on a complete representation of the many-body wavefunction will require a computer time that is exponential in the number of electrons. A typical example of such an approach is the configuration interaction (Cl) method, which expands the wavefunction in Slater determinants of one-body orbitals. Each time an atom is added to the system, an additional number of molecular orbitals must be considered, and the total number of determinants to reach chemical accuracy is then multiplied by this factor. Hence an exponential dependence of the computer time on the number of atoms in the system results. 

It is important to note that, at each level of coupled-cluster theory, we include through the exponential parameterization of Eq. (28) all possible determinants that can be generated within a given orbital basis, that is, all determinants that enter the FCI wave function in the same orbital basis. Thus, the improvement in the sequence CCSD, CCSDT, and so on does not occur because more determinants are included in the description but from an improved representation of their expansion coefficients. For example, in CCS theory, the doubly-excited determinants are represented by ]HF), whereas the same determinants are represented by (T2 + Tf) HF) in CCSD theory. Thus, in CCSD theory, the weight of each doubly-excited determinant is obtained as the sum of a connected doubles contribution from T2 and a disconnected singles contribution from Tf/2. This parameterization of the wave function is not only more compact than the linear parameterization of configuration-interaction (Cl) theory, but it also ensures size-extensivity of the calculated electronic energy. 

Circular Dichroism Vibrational Configuration Interaction Configuration Interaction PCI-X and Applications Density Functional Theory (DFT), Hartree-Fock (HF), and the Self-consistent Field Magnetic Circular Dichroism of n Systems Molecular Magnetic Properties Nucleic Acid Conformation and Flexibility Modeling Using Molecular Mechanics Spectroscopy Computational Methods Stereochemistry Representation and Manipulation. 

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