Applications of density functional theory

For Fig. 7.1 and Tables 7.1 and 7.2, for comparison with the presentations in Chapters 5 and 6, values from MP2/6-31G calculations (the standard post-Hartree Fock ab initio method Section 5.4.2) and from experiment (Fig. 7.1 [69], Fig. 7.2 [70]) were clearly necessary. This choice of the relatively small 6-31G basis is discussed below. The choice of DFT functionals required some consideration. B3LYP is retained from the first edition of this book because it continues to be very widely used. The pBP/DN functional/basis set (described in [68]) that was a feature of Spartan [71] and was used in the first edition of this book showed certain problems and is no longer available, and its replacement required some deliberation. The remaining choice was now narrowed to three functionals  

In our classification (7.2.3.4a-g) PBE is on rung three and TPSS is on rung four (these are rungs two and three if LDA and LSDA are collapsed into rung one). 

Qualitative conclusions from all this are reasonably good bond lengths (to within ca. 0.01 A) are given with the 6-31G basis by B3FYP, M06, and MP2 TPSS values (0.013 MAD error) are satisfactory for most purposes. All four 

3Personal communication from Professor J.P. Perdew, 2009 November 7. 

2 Energies Calculating Quantities Relevant to Thermodynamics and Kinetics 

Levine has compared geometries, energies, etc. from DFT with those from molecular mechanics, ab initio, and semiempirical methods [51]. Hehre [52] and Hehre and 

Geometry errors for 108 molecules were reported by Scheiner et al. [55], comparing several ab initio and DFT methods. They found that Becke s original three-parameter function (which they denote ACM, for adiabatic connection method B3LYP was developed as a modification of this [49]), with a 6-31G -type and with the 6-3IG  

Errors ate given as B3LYP BP/MP2. In some cases (e.g. MeOH) errors for two bonds are giv i, on one line and the line below. A minus 

Ramsay, F. J. Lovas, W. H. Laffeny, and A. G. Makai, Molecular Structures of Gas-Phase Polyatomic Molecules Determined by Spectroscopic Methods , J. Physical and Chemical Reference Data, 1979, S, 619-721. . Huang and K. Hedberg, J. Am. Chem. Soc., 1989, HJ, 6909. 

Hehre has compared bond lengths calculated by the DFT non-gradient-corrected SVWN method, B3LYP, and MP2, using the 6-31G (no polarization functions) and 

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The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. 

Chemical Applications of Density-Functional Theory B. B. Laird, R. B. Ross, T. Ziegler, Eds., ACS, Washington (1996). 

APPLICATIONS OF DENSITY FUNCTIONAL THEORY TO ELECTROCHEMICAL SYSTEMS... 

Blochl, P. E., Margl, P, Schwarz, K., 1996, Ab Initio Molecular Dynamics With the Projector Augmented Wave Method in Chemical Applications of Density Functional Theory, Laird, B. B., Ross, R. B., Ziegler, T. (eds.), American Chemical Society, Washington DC. 

Brown, S. T., Rienstra-Kiracofe, J. C., Schaefer, H. F., 1999, A Systematic Application of Density Functional Theory to Some Carbon-Containing Molecules and Their Anions , J. Phys. Chem. A, 103, 4065. 

Fan, L., Ziegler, T., 1992, Application of Density Functional Theory to Infrared Absorption Intensity Calculations on Main Group Molecules , J. Chem. Phys., 96, 9005. 

Principles and Applications of Density Functional Theory in Inorganic Chemistry II... 

Fan, L., and T. Ziegler. 1990. The application of density functional theory to the optimization of transition state structures. I. Organic migration reactions. J. Chem. Phys. 92, 3645. 

Applications of density functional theory to surface studies is given by ... 

For example, see the Proceedings of the Vlth International Conference on the Applications of Density Functional Theory, Paris, France, 29 Aug.-l Sept. 1995 [Int. J. Quantum Chem. 61, 181 (1997)]. 

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