Thermodynamics electronic structure calculations

As is well recognized, various macroscopic properties such as mechanical properties are controlled by microstructure, and the stability of a phase which consists of each microstructure is essentially the subject of electronic structure calculation and statistical mechanics of atomic configuration. The main subject focused in this article is configurational thermodynamics and kinetics in the atomic level, but we start with a brief review of the stability of microstructure, which also poses the configurational problem in the different hierarchy of scale. 

The final ingredient that enters the calculation is the density factor pw. This is the actual density of water appropriate to the thermodynamic state intended in the calculation. For the usual case of 1 atm. pressure and 298K, this is I gem 3. The reference density in the electronic structure calculations is p° = 1 atm//entropic cost of sequestering water in the metal-water complexes, the free energies should be adjusted by —mRT In (pi 2o/p ) = —mRTIn (1354). With these inputs the excess chemical potential is readily composed as per (9.50), provided the optimal value of m is known. This is found by composing the excess chemical potential for different assumed m values and identifying the most stable case. For the dication transition metals studied, this is found to be six, consistent with experiment [12]. 

In this chapter, the most common procedures for augmenting electronic-structure calculations in order to convert single-molecule potential energies to ensemble thermodynamic variables will be detailed, and key potential ambiguities and pitfalls described. Within the context of certain assumptions, this connection can be established in a rigorous way. 

In practice, then, it is fairly straightforward to convert the potential energy determined from an electronic structure calculation into a wealth of thennodynamic data - all that is required is an optimized structure with its associated vibrational frequencies. Given the many levels of electronic structure theory for which analytic second derivatives are available, it is usually worth the effort required to compute the frequencies and then the thermodynamic variables, especially since experimental data are typically measured in this form. For one such quantity, the absolute entropy 5°, which is computed as the sum of Eqs. (10.13), (10.18), (10.24) (for non-linear molecules), and (10.30), theory and experiment are directly comparable. Hout, Levi, and Hehre (1982) computed absolute entropies at 300 K for a large number of small molecules at the MP2/6-31G(d) level and obtained agreement with experiment within 0.1 e.u. for many cases. Absolute heat capacities at constant volume can also be computed using the thermodynamic definition... 

In particularly thorough examples of the traditional physical organic approach, Parker (1969) and Abraham (1974) interpreted solvent effects on Walden inversion reactions by using thermodynamic transfer functions. However, in order to explain the reaction rate decrease upon solvation from a microscopic point of view, quantum mechanical electronic structure calculations must be carried out. Micro-solvated Sn-2 reactions were initially studied in this way, with the CNDO/2 semiempirical molecular orbital (MO) method, by using the supermolecule... 

The introduction of the Cm-Parrinello method has not only extended the range of classical MD simulations based on empirical potentials but at the same time, it has also significantly increased the capabilities of conventional electronic structure calculations. Through the combination with a MD method a generalization to finite temperature and condensed phase systems was achieved. Furthermore, a whole set of simulation tools based on statistical mechanics can be apphed in this way in the context of an electronic structure method. Consequently, many dynamic as well as thermodynamic properties can be described within the accuracy of a first-principles method. 

Nelson DJ, Ashworth IW, Hillier IH, et al. Why is RCM favoured over dimerisation Predicting and estimating thermodynamic effective molarities by solution experiments and electronic structure calculations. Chem EurJ. 2011 17 13087-13094. 

First-principles thermodynamic calculations can be useful in this context by comparing the relative strength of chemisorption for different ions at the metal/environment interface and delineating the relevant thermodynamic conditions. First-principles thermodynamics involves the extrapolation of internal energies determined at OK via electron structure calculation to finite temperature free energies through the incorporation of vibrational, rotational, and translational enthalpic and entropic contributions as well as configurational effects. 

The calculations of LSM sohd solution considered here demonstrate the efficiency of use of thermodynamic formaUsm based on combination of the ab-initio electronic-structure calculations as developed in [754,756-758]. The main feature of this approach is the treatment of ordered superstructures presenting the La-Sr sublattice immersed in the field of the remaining lattice formed by Mn and O atoms. The total-energy calculations allow the formation energies of these superstructures for different compositions to be found and their competition at T =0 K to be analyzed. These calculations for a series of ordered structures permit extraction of the key energy parameters - the... 

Parameters of the molecular geometry, electronic structure and thermodynamic properties of the benzoyl peroxide (BPO) molecule and its symmetrical derivatives were calculated by the GAUSSIAN09 [9]. The molecular geometry optimization of all objects was carried out at the first stage of the work. The calculation of harmonic frequencies of vibrations and thermodynamic parameters were performed after that. The stationary points obtained after the molecular geometry optimization were identified as minima, as there were no negative values of analytic harmonic vibration frequencies for them. The reaction center of the peroxide compounds is a peroxide bond -0-0-. Therefore, selection criterion for the quantum chemical calculation method was the best reproduction of the peroxide moiety molecular geometry. 

Electronic structure calculations on the isomerization and epimerization of xylose to xylulose and lyxose by a zeolite Lewis acid catalyst suggest lyxose is formed from a stable intermediate and that xylulose is thermodynamically and kinetically favoured... 

Very recently we have communicated on the role of the 5f orbitals in bonding, aromaticity, and reactivity of planar isocyclic and heterocyclic uranium clusters [185]. Using electronic structure calculation methods (DFT) we demonstrated that the model planar isocyclic cjc/o-U X (n = 3, 4 X = 0,NH) and heterocyclic cjc/o-U (/u.2-X) (n = 3, 4 X = C, CH, NH) clusters are thermodynamically stable molecules with respect to their dissociation either to free U and X moieties or to their monomeric UX species. The equilibrium geometries of the cyclo- J X and cyclo-U iJ,2-X) clusters are shown in Fig.42. 

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