Examples of Ab Initio Calculations

Self-consistent-field and correlated calculations have now been made for a very large number of systems. The best way to judge the capabilities of these methods is to survey some of the results. 

The Hartree-Fock energies are estimated by extrapolating from more extensive basis sets, and represent the limit achievable for the SCF approach using a complete basis set. We can make the following observations  

The improvement in energy obtained when one goes from a single-f to a double- STO basis set is substantial, especially for atoms of higher Z. 

The disagreement between HF and exact energies (i.e., the correlation energy) grows progressively larger down the list. For neon it is almost 0.4 a.u. (10 eV), which is an unacceptable error in chemical measurements. 

One might think that the magnitude of the correlation energy in these examples would make SCF calculations on heavy atoms useless for quantitative purposes, but this 

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Examples of Ab Initio Calculations on Quasi-One-Dimensional Polymers... 

One of the powers of ab initio calculations is that they may provide information about features included in the models to be used to interpret experimental data. For each of the topics described above in Section 4, we give specific examples of ab initio calculations related to measurements obtained with these experimental techniques. The thrust of the description of these examples is to relate bond character to its consequences for observable quantities. While cluster calculations require considerable computational resources, our focus is on the analysis of the wavefunctions rather than on the computation details, which are given in appropriate references. The organization of the material on this section follows that used in the previous section. 

Now, we discuss briefly the situation when one or both of the adiabatic electronic states has/have nonlinear equilibrium geometry. In Figures 6 and 7 we show two characteristic examples, the state of BH2 and NH2, respectively. The BH2 potential curves are the result of ab initio calculations of the present authors [33,34], and those for NH2 are taken from [25]. 

Nitrones are a rather polarized 1,3-dipoles so that the transition structure of their cydoaddition reactions to alkenes activated by an electron-withdrawing substituent would involve some asynchronous nature with respect to the newly forming bonds, especially so in the Lewis acid-catalyzed reactions. Therefore, the transition structures for the catalyzed nitrone cydoaddition reactions were estimated on the basis of ab-initio calculations using the 3-21G basis set. A model reaction indudes the interaction between CH2=NH(0) and acrolein in the presence or absence of BH3 as an acid catalyst (Scheme 7.30). Both the catalyzed and uncatalyzed reactions have only one transition state in each case, indicating that the reactions are both concerted. However, the synchronous nature between the newly forming 01-C5 and C3-C4 bonds in the transition structure TS-J of the catalyzed reaction is rather different from that in the uncatalyzed reaction TS-K. For example, the bond lengths and bond orders in the uncatalyzed reaction are 1.93 A and 0.37 for the 01-C5 bond and 2.47 A and 0.19 for the C3-C4 bond, while those in... 

Theoretical calculations have been carried out on a number of zinc-containing enzymatic systems. For example, calculations on the mechanism of the Cu/Zn enzyme show the importance of the full protein environment to get an accurate description of the copper redox process, i.e., including the electronic effects of the zinc ion.989 Transition structures at the active site of carbonic anhydrase have been the subject of ab initio calculations, in particular [ZnOHC02]+, [ZnHC03H20]+, and [Zn(NH3)3HC03]+.990... 

Semi-empirical methods, such as those outlined in Appendix F, use experimental data or the results of ab initio calculations to determine some of the matrix elements or integrals needed to carry out their procedures. Totally empirical methods attempt to describe the internal electronic energy of a system as a function of geometrical degrees of freedom (e.g., bond lengths and angles) in terms of analytical force fields whose parameters have been determined to fit known experimental data on some class of compounds. Examples of such parameterized force fields were presented in Section III. A of Chapter 16. 

Rather few papers have dealt with the computation of thermodynamic functions from the results of ab initio calculations, but for H2, where the latter are of spectroscopic accuracy, Kosloff, Levine, and Bernstein have computed the thermodynamic properties of Ha, Da, and HD, using the best theoretical results.75 This work represents the first example of an accurate determination of a bulk, macroscopic property from first principles. 

CH2, the next hydride in the series, is the classic example of the power of ab initio calculations in that the clear prediction was of a non-linear geometry, and this led to a consequent revision of the experimental data by Herzberg. Several recent calculations on this species should be mentioned. 

Ground State of CO. The CO molecule has been extensively studied, both experimentally and theoretically. Table 14 compares ground-state 02+) spectroscopic constants calculated by the Hartree-Fock method109 and by the density functional approach99 with experiment.104 In addition to these spectroscopic constants, the polar nature of the molecule provides a further measurable quantity, the dipole moment. Since the intensities of infrared vibration-rotation bands allow the dipole moment to be determined as a function of C-O separation this provides a useful comparison with the results of ab initio calculations. For example, the positive sign obtained from the equilibrium dipole moment by Hartree-Fock calculations was viewed as a reason to question the negative value found experimentally, whereas the current view is that the positive sign is a defect of the Hartree-Fock method. 

Advances in the development of theoretical methods and computer construction are indispensable for the growing feasibility of ab initio calculations, but this alone does not guarantee a future widespread use of ab initio calculations by chemists in solving their problems. What is demanded by chemists is a high predictive power of theory in various branches of chemistry, A classical example of how the ab initio calculations should meet the needs of chemists was provided as early as in 1967 by dementi and Gayles " in their study on the complex NH. HCl, The calculation of the potential hypersurfaces and a detailed analysis of wave functions of both the complex and the dissociation components showed that NH Cl may exist in the gas phase. For the first time, the results of ab initio calculations were used for the evalua-tion of the equilibrium constant for a chemical reaction. Predicted equilibrium constants for the process NH2(g) + HCl(g) NH Cl(g) at different temperatures suggested the experimental conditions at which... 

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