Total energy difference method

The BS plus spin projection method discussed here is closely connected to the simple open-shell singlet method for optical excitations based on the Slater sum rule and ASCF (self-consistent-field total energy difference method). The mixed spin excited state is like the BS state, also of mixed spin. The Slater sum rule method" " is also quite effective for multiplet problems for excited states of transition metal complexes as shown in the work of Dahl and Baerends. ... 

In the case of crystals, both intramolecular (conformational) and packing energies should be taken into account simultaneously. Such a total energy minimization method, with suitable crystallographic constraints, has been applied in different steps of the analysis of crystalline structures of three different synthetic polymers. Structures of these molecules, namely, isotactic trans-1,4-poly-penta-1,3-diene (ITPP), poly-pivalolactone (PPVL), and isotactic cis-1,4-poly(2-methyl-penta-1,3-diene)(PMPD), do not have troublesome features such as charged groups, counterions, and solvent molecules. 

Electronic d d excitations at the NiO(lOO) surface have been calculated either with the Cl method on small clusters [80-82], or with a periodic ab initio HF method by means of total energy differences [83]. Both ap-... 

Ni v clusters have been the subject of very many theoretical studies (see, e.g., 33 and references therein). Wetzel and DePristo80 studied Ni clusters for 24 < N < 55 using the so-called effective-medium potential which is similar to the embedded-atom methods described above. They used a molecular-dynamics approach in optimizing the structure, and identified particularly stable structures through the total-energy difference between the energetically two lowest isomers for a given N, i.e., AUE(N) of Eq. (51). 

In our own work,33 that we here shall discuss briefly, we used the embedded-atom potential together with the Aufbau/Abbau method of Section 2.8 in optimizing the structure. The stability function, A2E(N), Eq. (50), is shown in Figure 18. It shows a set of peaks that correspond to particularly stable clusters. It is interesting to notice that if one instead studies the total-energy difference... 

The second major route to interpret photoelectron spectra has been via the computation of total energy differences. As noted in Section 3.2, this is fully Justified for selected states. The lowest-energy peak corresponds, for instance, to the IP (if the initial state is neutral) or to the EA (for anionic species). In both cases, the corresponding excitation energy can be computed as a difference of ground-state energies, and this is well within the reach of DFT methods. 

In the dielectric screening method the electron density response due to the motion of the ions around their equilibrium positions is calculated in first order perturbation theory. The potential energy of the crystal for an arbitrary configuration of the ions is expanded to second order in the ionic displacements from equilibrium. The expansion coefficients of the second order term form a matrix. The Fourier transform of this matrix is the dynamical matrix whose eigenvalues yield the phonon frequencies. The dynamical matrix has an ionic and electronic part. The electronic part can be expressed in terms of the electron density response matrix and of the ionic potential. This method has the advantage over the total energy difference m ethod that the phonon frequencies for any arbitrary wave vector can be calculated without additional difficulties. Furthermore in this method the acoustic sum rule is automatically satisfied as a consequence of the way the dynamical matrix is derived. However the dielectric screening method is limited to harmonic phonons. 

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