Composite methods for energy calculations

The Gaussian-3 (G3) method (so called because it is an improvement on its predecessors, the G1 and G2 methods) is designed to give a result close to what would be obtained by a QCISD(T)/G31arge calculation in much less computer time than required by such a 

G3//B3LYP (also called G3B3 or G3B) is a modification of G3 that uses geometries and zero-point vibrational energies found from B3LYP/6-31G calculations instead of from MP2/6-31G and HF/6-31G calculations [A. G. Baboul, J. Chem. Phys., 110,7650 (1999)]. G3//B3LYP is faster than G3 and just as accurate as G3. 

G3X (where the X stands for extension) is an improvement of the G3 method. It uses B3LYP/6-31G(2df,p) geometries and zero-point energies and adds a g polarization function to the G3Large basis set for second- and third-row atoms [L. A. Curtiss et al., J. Chem. Phys., 114, 108 (2001)]. For the G3/05 test set, the mean absolute deviation of calculated values from experimental values is 1.01 kcal/mol for G3X and 1.13 kcal/mol for G3 [L. A. Curtiss et al., J. Chem. Phys., 123, 124107 (2005)]. 

A desirable goal is to compute a thermodynamic energy such as the molecular atomization energy or the enthalpy of formation, with chemical accuracy, which means an accuracy of 1 kcal/mol. Currently available functionals in DFT cannot do this. High-level methods such as CCSD(T), QCISD(T), CISDTQ, and MP6 with large basis sets can do this but are much too costly to be feasible except for quite small molecules. The aim of the compound methods G3 and CBS discussed in this section is to achieve 1 kcal/mol accuracy with a computational time that allows calculations on molecules containing several nonhydrogen atoms. 

Curtiss et al., /. Chem. Phys., 94,7221 (1991)], the predecessor of G3, uses larger basis sets in most of the single-point calculations, and so is slower than G3. G3 uses a full MP2/G31arge calculation, whereas the corresponding calculation in G2 is a frozen-core MP2 calculation. G3 includes spin-orbit corrections for atomic energies, which G2 did not. G2 uses the same higher-level correction for atoms as for molecules. 

The MP4 calculations are the most time-consuming steps in the G2 and G3 methods and limit their applicability to rather small molecules. The G2(MP2) and G3(MP2) 

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Comments Energy balances involving mixtures are performed in the same manner as for pure fluids. All that is required is a method for the calculation of enthalpy and entropy at given pressure, temperature, and composition. 

Since analytic second derivatives are available for MP2 calculations, numerical difference calculations of CCSD(T) energies are only required for a relatively small basis set. This type of basis set correction approximation is also available in Grow. It is not possible to use some composite methods which, like the G2 and G3 schemes,66 involve adding non-differentiable corrections to the estimated electronic energy. However, there are other recently developed composite methods which might be effectively employed to construct this type of interpolated PES.67... 

There now exist several methods for predicting the free energy associated with a compositional or conformational change.7 These can be crudely classified into two types "exact" and "approximate" free energy calculations. The former type, which we shall discuss in the following sections, is based directly on rigorous equations from classical statistical mechanics. The latter type, to be discussed later in this chapter, starts with statistical mechanics, but then combines these equations with assumptions and approximations to allow simulations to be carried out more rapidly. 

In this book, the experts who have developed and tested many of the currently used electronic structure procedures present an authoritative overview of the theoretical tools for the computation of thermochemical properties of atoms and molecules. The first two chapters describe the highly accurate, computationally expensive approaches that combine high-level calculations with sophisticated extrapolation schemes. In chapters 3 and 4, the widely used G3 and CBS families of composite methods are discussed. The applications of the electron propagator theory to the estimation of energy changes that accompany electron detachment and attachment processes follow in chapter 5. The next two sections of the book focus on practical applications of the aforedescribed... 

As stated, the most commonly used procedure for temperature and composition calculations is the versatile computer program of Gordon and McBride [4], who use the minimization of the Gibbs free energy technique and a descent Newton-Raphson method to solve the equations iteratively. A similar method for solving the equations when equilibrium constants are used is shown in Ref. [7],... 

Energies calculated for the EH and CNDO models are approximations, and are more important for indicating trends within a series than for giving absolute numbers. They do suggest that the answer as to which is trapped first, the electron or the silver ion, could depend on the substrate site and the size and composition of the nucleus, Calculations by the semiclassical method likewise give only approximate values, and the amount of the approximation is unknown. 

An alternative is to use the tridiagonal method for calculating compositions, but to calculate the new temperatures directly, without iterating on the bubble-point equation, These new temperatures are approximate but as long as the internal compositions are properly corrected during each column trial, the temperature profile will continue to move toward the solution. This is the basis of the theta method of Holland (7, 9, 26). With either alternative, the energy balances are used to find the total flow rates. 

The concept of acidity and basicity in mixed solvents is discussed and a method for analyzing differential solvation effects is described. This enables the free energy of transfer of the proton between water and the mixed solvent, AGt°(H+), to be calculated, and thereby AGt°fi) for i = X" and M+, using values for AGt°(HX) and AGt°(MX). The pKa values for acids are combined with AGt°(H+) to calculate proton affinities in mixed solvents, and these are used as measures of free energies of transfer of the charges on the molecular species, AGt°(i)e. Values of AGt°(i) and AGt°(i)e are compared for a range of co-solvents and the factors influencing the way these quantities vary with solvent composition are discussed. 

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