Ab-Initio Molecular Orbital Methods

Unlike experimental methods of structure analysis, there is no basis for estimating the error associated with a particular calculation. There is therefore an art, based on experience, in deciding the best level of approximation versus computing 

Acronyms for Successive Levels of Approximations Used in Ab-Initio LCAO-MO I Gaussian Methodology [2S3] 

Molecular orbitals from linear combination of atom orbitals Spin-restricted Hartree-Fock. Wave function constructed from antisymmetrized product of doubly occupied spin orbitals (UHF, spin-unrestricted Hartree-Fock calculations are used for excited states and radicals) 

Slater-type orbitals, represented by a Gaussian also referred to as minimal basis 

Split-valence or double zeta. Orbitals represented by 3 Gaussians near the nucleus and 2 away from the nucleus. Hydrogen atoms represented by one Gaussian. This is a good basis for conformational analysis of moderate-sized molecules 

QUANTUM CHEMICAL METHODS Ab Initio Molecular Orbital Methods 

Since the early 1970s when ab initio molecular orbital calculations became routine, one of the major goals of modern quantum chemistry has been the prediction of molecular thermochemical data to so-called chemical accuracy ( 1 kcal/mol). One of the problems was that the Hartree-Fock calculations done in the 1970s gave large errors (up to 100 kcal/mol) in bond energies. Prediction of accurate thermochemical data required going beyond Hartree- 

As described earlier, ab initio molecular orbital methods12-17 for prediction of thermochemical data can be divided into three categories (1) those using very high level calculations with extrapolation, (2) those implementing moderate level calculations with molecule-independent parameters, and (3) those of moderate level calculations with molecule-dependent parameters. In this section we discuss some aspects of these different approaches. 

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The cornerstone of semiempirical and ab initio molecular orbital methods is the Harhee equation and its extensions and variants, the Harhee-Fock and Roothaan-Hall equations. We have seen that the Hamiltonian for the hydrogen atom. 

Oxirane (1) and methyloxirane (3) are miscible with water, ethyloxirane is very soluble in water, while compounds such as cyclopentene oxide and higher oxiranes are essentially insoluble (B-73MI50501) (for a discussion of the solubilities of heterocycles, see (63PMH(l)l77)). Other physical properties of heterocycles, such as dipole moments and electrochemical properties, are discussed in various chapters of pmh. The optical activity of chiral oxiranes has been investigated by ab initio molecular orbital methods (8UA1023). 

Ohta K, Kamada K (2006) Theoretical investigation of two-photon absorption allowed excited states in symmetrically substituted diacetylenes by ab initio molecular-orbital method. J Chem Phys 124 124303... 

Use of high-level ab initio molecular orbital methods or density functional Hamiltonians to simulate the QM region through approximate solutions of the electronic Schrodinger equation. 

Overview of Semi-Empirical and Ab Initio Molecular Orbital Methods. 2.2 Applications of Molecular Mechanics. 3 Experimental Structural Methods. 3.1 X-Ray Diffraction. 3.2 NMR Spectroscopy and. 3.3 Mass Spectrometry. 3.4 UV/Fluorescence. 3.5 IR Spectroscopy. 3.6 Redox Potentials. 4 Thermodynamic Aspects. 4.1 Melting Points. 5 Reactivity of Fully Conjugated Rings 6 Reactivity of Nonconjugated Rings... 

Overview of Semi-Empirical and Ab Initio Molecular Orbital Methods... 

Theoretical studies have been carried out for the gas-phase nucleophilic ring-opening of 3,4-epimino-, 3,4-epoxy-, and 3,4-epithio-but-l-ene.88 Attack by HCP on a-C, y-C, and <5-C was examined by using VIP2/6-31+G //M P2/6-31+G ab initio molecular orbital methods. 

AI, ab initio molecular orbital methods DF, density functional methods SE, semiempirical molecular orbital methods FF, force field methods. 

Table 5 Average Absolute Deviations (in kcal/mol) from Experiment of Various Composite Ab Initio Molecular Orbital Methods for Ionization Energies, Electron Affinities, Proton Affinities, and Enthalpies of Formation in the G2/97 Test Set"... 

Finally we describe several methods that combine molecule-dependent empirical parameters with a moderate level ab initio molecular orbital method. The BAC-MP4 method of Melius and coworkers115-118 combines a computationally inexpensive molecular orbital method with a bond additivity correction. This procedure uses a set of accurate experimental data to obtain a correction for bonds of different types that is then used to adjust calculated thermochemical data such as enthalpies of formation. Quite accurate results can be obtained if suitable reference molecules are available and if the errors in the calculation are systematic. The computational methodology is based on an MP4/6-31G(d,p)//HF/6-/31G(d) calculation. A pairwise additive empirical bond correction is derived for different bonds from fitting to experimental enthalpies of formation or in some cases to high quality ab initio computations. In addition, for open-shell molecules an additional correction is needed to compensate for spin contamination of the wavefunction from higher spin states in the unrestricted Hartree-Fock (UHF) method. 

Theoretical chemistry at UBC was further strengthened with the arrival of Delano Chong and Keith Mitchell in 1965 and 1966, respectively. Chong s interests in quantum chemistry have spanned the full range from semiempirical to ab initio molecular orbital methods. His long-standing interests in perturbation methods and constrained variations have figured prominently in his publications. He is probably best known for his attempts to calculate the X-ray and UV photoelectron spectra of molecules, often by means of perturbation corrections to Koopmans theorem.40 More recently he has shifted his focus to coupled pair functional methods and density functional methods, with a special interest in polarizabilities and hyperpolarizabilities.41... 

Drs. Larry A. Curtiss, Paul C. Redfern, and David J. Frurip present a tutorial on how to compute enthalpies of formation in Chapter 3. Often a computational chemist will want to know how stable a molecule is. The techniques described in this chapter can answer this question. The authors, who have studied what has been called computational thermochemistry, describe ab initio molecular orbital methods (including the highly accurate and popular Gn methods), density functional methods, semiempirical molecular orbital methods, and empirical methods (such as based on bond energies). These methods are richly illustrated with detailed, worked out examples. 

These slight differences are mainly due to the smearing of electron density caused by thermal vibration of the Co atom in crystals. Johansen has also calculated the theoretical deformation density of Co0610 by the ab initio molecular orbital method (39), on the assumption of a regular octahedral geometry with high-spin state (t2g )Heg)2. The as-phericity of 3d electron density is similar to that observed for [Co(N02)6]3. ... 

Another way of performing calculations using the cluster model is the use of a hybrid method. It is a theoretical method, which uses different approaches for different parts of the molecular system. The ONIOM method is one of the hybrid methods developed quite recently to facilitate accurate ab initio calculations of large chemical species. The ONIOM method (n-layered integrated molecular orbital and molecular mechanics approach) [29] is a multi-level extrapolation method, in which the studied molecular system is divided into two or more parts or layers. The most important part of the system from the chemical point of view (the inner part, IP) is treated at a high" level of theory (the HL method - a high level of ab initio molecular orbital method) and the rest of the system is described by a computationally less demanding method (the LL method - the lowest ab initio approximation or even semiempirical or molecular mechanic approximations) [30]. 

Dorsett, H., White, A., Overview of Molecular Modelling and ab Initio Molecular Orbital Methods Suitable for Use with Energetic Materials, Technical Report, Def. Sci. Technol. Organ. DSTO-GD-0253, i-iv, 1-35, Weapons Systems Division, Aeronautical and Maritime Research Laboratory, Melbourne, Australia, 2000... 

Molecular orbital calculations can provide the optimized structure and indicate the thermodynamic relative stabilities. Nakamura et al21 reported the results of an ab initio calculation of spironaphthoxazine, focusing on the determination of the most stable structure of the colored form. Figure 2.7 shows the optimized structure of the four open forms by using the ab initio molecular orbital method (HF 6-31G /3-21G). 

In a-cyanoacetohydrazide, where there is both strong inter- and intramolecular hydrogen bonding and large dipole interactions, the conformer observed in the crystal is the eighth highest in calculated energy, with a difference of 37 kJ mol-1 over the minimum calculated by ab-initio molecular orbital methods [267]. 

For hydrogen bonds weaker than OH 0=C or NH 0=C, theory predicts smaller differences in the X-H bond lengths and negligible changes in the nonhydrogen bonds. TWo models have been studied theoretically with the ab-initio molecular orbital method at the HF/3-21G level of approximation. These are formaldehyde oxime cyclic dimer versus the monomer [378] and formaldehyde hydrazone cyclic dimer versus the monomer [379]. Except for the O-H and N-H bonds, these differences are too small to be detected by single crystal X-ray or neutron diffraction methods, as shown in Fig. 5.2. 

Nine energy-minimum structures of 1,5-dithiacyclooctane 810 (DTCO) were obtained by the ab initio molecular orbital method (6-31G ) the most stable was a twist-boat-chair structure (TBC) while the BC conformer, in which... 

Such a consensus approach is reminiscent of what some computational chemists were doing in the the 1970s and 1980s when they were treating each molecule by not one, but several available semiempirical and ab initio molecular orbital methods, each of which gave different—and less than perfect—predictions of molecular properties. 

Ab initio quantum mechanical (QM) calculations represent approximate efforts to solve the Schrodinger equation, which describes the electronic structure of a molecule based on the Born-Oppenheimer approximation (in which the positions of the nuclei are considered fixed). It is typical for most of the calculations to be carried out at the Hartree—Fock self-consistent field (SCF) level. The major assumption behind the Hartree-Fock method is that each electron experiences the average field of all other electrons. Ab initio molecular orbital methods contain few empirical parameters. Introduction of empiricism results in the various semiempirical techniques (MNDO, AMI, PM3, etc.) that are widely used to study the structure and properties of small molecules. 

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