Energies and molecular properties

Derivatives of the energy and molecular properties are most conveniently calculated in Cartesian coordinates. Due to translational and rotational symmetries these Cartesian derivatives are not independent. For example, for forces only 3N — m (m = 5, 6) Cartesian components are independent. The remaining five or six components can be calculated by taking into consideration the translational and rotational symmetries of the energy. This has two useful applications. First, the number of derivatives that must be calculated ab initio may be reduced. This saving is especially important for small molecules. Alternatively, one may calculate all derivatives ab initio and simply use translational and rotational symmetries as a simple check on the calculation. 

In order to investigate the energies and molecular properties of molecules interacting with aerosol particles, it is crucial to establish the Hamiltonians and the energy functionals for the two structural environment methods. The basic principle for both structural environment methods is the same and it is one that has been utilized successfully within quantum chemistry [2-33] and molecular reaction dynamics [19,68-71,96], we divide a large system into two subsystems. The focus is... 

Hamiltonian with the zeroth-order wave function) saves considerable computational time at the cost of rather small errors in the DFT energy and molecular properties. However, it is preferable that the KS orbitals be found using the same functional that is used to calculate the energy. When this is done, one says the calculation has been performed self-consistently. 

For example, this method reveals a high correlation coefficient between measured capacity ratios and the sum of theoretically calculated molecular interaction energy and molecular property values, opening the possibility for quantitative analysis of chromatographic retention mechanisms. 

Z.-M. Xue, Y.-Z. Ding, C.-H. Chen, Electrochim. Acta 2007, 53, 990-997. A DPT study of electronic structures, energies, and molecular properties of lithium bis[croconato]borate and its derivatives. 

Before starting properly with perturbation theory we will first introduce in the next section the Hellmann Feynman theorem, which establishes a deep connection between the energy and molecular properties calculated as expectation values and that does not rely on perturbation theory. 

All molecular properties are related to the electron density p, directly or indirectly. DFT is based on the Hohenberg-Kohn theorem which states that energy and molecular properties are uniquely determined by the electron density. Electron density is a physical observable, and is the simplest one-electron... 

Explicitly correlated ri2-dependent electronic wave functions allow for a very accurate treatment of energies and molecular properties, that is, a few orders of magnitude more accurate than the usual Cl expansions in terms of antisymmetrized products of one-particle orbitals. 

In previous publications we have described the application of the linked-diagram-based methods, many-body perturbation theory and coupled-cluster double-excitation theory, for the computation of potential energy surfaces, electronic excitation energies, and molecular properties. Here we report details of potential energy surface features for two species commonly found in flames formyl radical, HCO, and hydrogen nitroxide, HNO. In particular, we... 

---