Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.

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Coupled-cluster theory in quantum chemistry

The method of natural localized molecular orbitals (NLMOs) is presented as a novel and efficient technique for obtaining LMOs for SCF and CI wave functions. It is an extension of the previously developed natural atomic orbital (NAO) and natural bond orbital (NBO) methods, and uses only the information contained in the one‐particle density matrix. Results are presented for methane and cytosine to indicate that NLMOs closely resemble LMOs obtained by the Boys and Edmiston–Ruedenberg methods, with the exception that the NLMO procedure automatically preserves the MO σ–π separation in planar molecules. The computation time is modest, generally only a small fraction of the SCF computation time. In addition, the derivation of NLMOs from NBOs gives direct insight into the nature of the LMO ‘‘delocalization tails,’’ thus enhancing the role of LMOs as a bridge between chemical intuition and molecular wave functions.

Natural localized molecular orbitals

A new intrinsic localization algorithm is suggested based on a recently developed mathematical measure of localization. No external criteria are used to define a priori bonds, lone pairs, and core orbitals. It is shown that the method similarly to Edmiston–Ruedenberg’s localization prefers the well established chemical concept of σ–π separation, while on the other hand, works as economically as Boys’ procedure. For the application of the new localization algorithm, no additional quantities are to be calculated, the knowledge of atomic overlap intergrals is sufficient. This feature allows a unique formulation of the theory, adaptable for both ab initio and semiempirical methods, even in those cases where the exact form of the atomic basis functions is not defined (like in the EHT and PPP calculations). The implementation of the procedure in already existing program systems is particularly easy. For illustrative examples, we compare the Edmiston–Ruedenberg and Boys localized orbitals with those calculated b...

A fast intrinsic localization procedure applicable for ab initio and semiempirical linear combination of atomic orbital wave functions

Fragmentation Methods: A Route to Accurate Calculations on Large Systems Mark S. Gordon,* Dmitri G. Fedorov, Spencer R. Pruitt, and Lyudmila V. Slipchenko Department of Chemistry and Ames Laboratory, Iowa State University, Ames Iowa 50011, United States Nanosystem Research Institute, National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, United States

Fragmentation methods: a route to accurate calculations on large systems.

Anisotropy of the Induced Current Density (ACID), a General Method To Quantify and Visualize Electronic Delocalization

Coupled-cluster studies. II. The role of localization in correlation calculations on extended systems

Within the simple displaced oscillator state ansatz of Davydov [Phys Scr 20, 387 (1979)], called the ${\mathit{D}}_{2}$ ansatz state, the soliton remains stable against strong disorder in the sequences of masses, spring constants, and coupling constants However, weak diagonal disorder or disorder in the dipole coupling constants destroys the solitons Within the ${\mathit{D}}_{1}$ ansatz, in which the quantum nature of the lattice plays a greater role than in the classical ${\mathit{D}}_{2}$ state, the soliton appears only from nonlinearities roughly 3 to 4 times larger than those in ${\mathit{D}}_{2}$ models The sensitivity of such solitons to disorder is practically opposite that for the ${\mathit{D}}_{2}$ state Within the partial dressing model we find only dispersing solitary waves, no real traveling solitons The sensitivity of such waves to disorder is similar to the ${\mathit{D}}_{1}$ case

Quantum and disorder effects in Davydov soliton theory.

Vibrational spectra of cyclohexanecarboxaldehyde are calculated with density functional theory using the B3LYP functional together with a 6-311++G** basis set and presented. The results in the case of the infrared spectrum of the mixture of conformers at 300 K are compared with the experimental spectrum and, apart from the intensities of the CH and CO stretches, reasonable agreement is found. These deficiencies can be traced back to the well-known nonlinearities in case of CH stretches and the CO stretch. Potential energy distributions among symmetry coordinates in each normal mode are presented and used to assign specific atomic movements to each of the modes. Potential energy scans for the CHO rotor in both the axial and equatorial conformers are presented and barrier heights are compared with previous Hartree–Fock calculations and experimental data. It is reported that there could be three stable conformers, namely equatorial-gauche (eg), which is the most stable, equatorial-trans (et) and axial-gauche (ag). The optimized energies of all the minima and of the transition states are presented. However, comparison of the calculated spectrum with the experimental one indicates that total energies are slightly in error and that in the mixture of conformers no ag is present and thus the et to eg ratio is also different. Using experimental values for relative energies of conformers, we could obtain spectra in fair agreement with experiment. This indicates that when only total energy differences are calculated, slight errors in them play a role because of the very small relative energies in this case, while properties like geometries and spectra, which depend not on energy differences but on analytically calculated energy derivatives, are not affected.

Theoretical vibrational spectra of cyclohexanecarboxaldehyde

We present the formalism for the correction of the band structure for correlation effects of polymers in the framework of a localized orbital approximation, using the quasiparticle model. For this purpose we use in an ab initio framework Mo/ller–Plesset perturbation theory in second order, the coupled cluster doubles method, and its linear approximation. The formalism is applied to a water stack and two different forms of a water chain as model systems to test the reliability of the approximations involved. From our previous work we know that, e.g., in polyacetylene difficulties due to the localizability of the canonical crystal orbitals do not arise from the π or π* bands, but from bands of σ symmetry. Thus we concentrate in this work again on polyacetylene as an example of a realistic polymer. We find that the localized orbital approximation is quite useful also in the case of band structure corrections due to correlation effects. However, the coupled cluster calculations, in particular, turn out to be ...

Numerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene

Wolfgang Förner

Papers

Coupled-cluster studies. II. The role of localization in correlation calculations on extended systems

Quantum and disorder effects in Davydov soliton theory.

Theoretical vibrational spectra of cyclohexanecarboxaldehyde

Numerical application of the coupled cluster theory with localized orbitals to polymers. IV. Band structure corrections in model systems and polyacetylene

Analysis of the infrared and Raman spectra of phenylacetic acid and mandelic (2-hydroxy-2-phenylacetic) acid.