Making More Extensive Use of the Coupled-cluster Wave Function: from the Standard Energy Expression to the Energy Expectation Value

The standard coupled-cluster (CC) scheme with single and double excitations in the cluster operator (CCSD) includes only up to quadruple excitations in the equations. The CCSD exponential expansion generates, however, all possible excitations out of the reference function through products of the cluster operators. Clearly, in all standard approximate CC approaches only a part of the CC wave function is used in the equations. If the standard CCSD wave function is inserted into the energy expectation value expression then the complete CCSD wave function contributes to the energy. Such an energy expectation value expression can be presented as a sum of the standard CCSD energy formula plus correction terms. The correction terms provide an information about the quality of the total CC function. Contributions associated with the presence of higher than double excitations in the bra CCSD wave function supplement the CCSD energy obtained within the standard scheme. These contributions can be generated in a sequential way by considering intermediate excitation levels for the bra CCSD wave function in the expectation value expression before reaching the highest excitation level. In this way the importance of particular components differing in the standard and expectation value CCSD energies can be investigated. Some of the contributions can be recognized as close to or identical with the so-called renormalized noniterative corrections to the CC methods. We try to see to what an extent the nonstandard energy expressions, like the energy expectation value or the asymmetric energy formula, can be used to extend the applicability of the CCSD method illustrating our considerations with some numerical examples.Dedicated to Professor Jean-Paul Malrieu to honor his contribution to quantum chemistry and physics     

Application of a thermogravimetric technique for the determination of low nitrogen solubilities in metals: Using iron as an example

A thermogravimetric technique was explored in order to precisely investigate the low nitrogen solubilities in metals. The thermogravimetry (TG) set-up is presented in detail. By the optimization of the set-up, a good baseline (noise level <2 μg, curve drift: ±1–4 μg/h) was obtained. The measurements of nitrogen solubility in iron are described. The weight signal arising from the nitrogen dissolved in iron was recorded continuously as a function of time under various experimental conditions. The nitrogen solubility can be calculated from the weight change between the beginning of nitrogen introduction and the steady state (equilibrium). There is a good agreement between the present measurements and the data in the literature determined by alternative methods such as chemical analyses of quenched samples, Sieverts’ method as well as thermogravimetric technique. In addition, a so-called isothermal stepping TG process shows that the TG set-up has a sufficient sensitivity to display the effect of the phase transformation of iron from body-centered cubic phase to face-centered cubic phase on the nitrogen solubility.     

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