DMRG-SCF study of the singlet, triplet, and quintet states of oxo-Mn(Salen)

We use CheMPS2, our free open-source spin-adapted implementation of the density matrix renormalization group (DMRG) [Wouters et al., Comput. Phys. Commun. 185, 1501 (2014)], to study the lowest singlet, triplet, and quintet states of the oxo-Mn(Salen) complex. We describe how an initial approximate DMRG calculation in a large active space around the Fermi level can be used to obtain a good set of starting orbitals for subsequent complete-active-space or DMRG self-consistent field (CASSCF or DMRG-SCF) calculations. This procedure mitigates the need for a localization procedure, followed by a manual selection of the active space. Per multiplicity, the same active space of 28 electrons in 22 orbitals (28e, 22o) is obtained with the 6-31G*, cc-pVDZ, and ANO-RCC-VDZP basis sets (the latter with DKH2 scalar relativistic corrections). Our calculations provide new insight into the electronic structure of the quintet.Comment: 5 pages, 4 figures, 2 tables; submitted to J. Chem. Phy

Explicitly correlated trial wave functions in Quantum Monte Carlo calculations of excited states of Be and Be-

We present a new form of explicitly correlated wave function whose parameters are mainly linear, to circumvent the problem of the optimization of a large number of non-linear parameters usually encountered with basis sets of explicitly correlated wave functions. With this trial wave function we succeeded in minimizing the energy instead of the variance of the local energy, as is more common in quantum Monte Carlo methods. We applied this wave function to the calculation of the energies of Be 3P (1s22p2) and Be- 4So (1s22p3) by variational and diffusion Monte Carlo methods. The results compare favorably with those obtained by different types of explicitly correlated trial wave functions already described in the literature. The energies obtained are improved with respect to the best variational ones found in literature, and within one standard deviation from the estimated non-relativistic limitsComment: 19 pages, no figures, submitted to J. Phys.

Estimation of stress intensity factors in ship structural connections

Stiffened plated structures such as ships and box girder bridges, result in connection details that contain sharp internal corners. Many failures in ship structure have been found to be associated with fatigue crack propagation at the side shell connections between longitudinal and transverse structure. According to elastic stress analysis, these sharp corners are geometric singularities that have an infinite stress in the corner. A further complication of stiffened structures is that a crack may grow through intersections, e.g. of plates and stiffeners and changes of plate thickness before it causes a catastrophic structural failure. In this thesis, a new approach is developed to simplify the analysis of these issues. The singular stress contribution is, as usual, characterised by Y, the non-dimensional the stress intensity factor but within this method simplified analysis is used to calculate the Y values. The method combines a ratio of non-singular linearized ligament stresses to estimate the effect of large changes in crack length and changes in plate thickness with an empirical methods to estimate the local effect as the crack grows through a change of thickness. The method does not require an analysis of the actual singularity, so saving analysis time and, importantly, giving the engineer some feeling for the result and the possibility of a “back of the envelope” calculation for the SIF or Y. This work is based on running finite element analyses, to determine the Stress Intensity Factor and Y and using the results to test the empirical or analytical methods.The derived methods are useful both for assessment of existing structures and for design application. Comparing the results from the application of this new methodology with the FE method and existing fatigue analysis guidance, the new method is very much quicker and easier to apply. It is though less accurate than FE analysis and so is most appropriate for, (1) preliminary assessment, (2) reliability assessment where many structural and defect variations are to be considered and (3) for checking whether a more detailed analysis is producing sensible results. For design calculations often a stress concentration factor or SCF is needed that can be used with an S-N curve. The actual predicted peak stress and hence SCF will, for finite element analysis, depend on the element size and will normally increase as the element size decreases. The existing guidance on determining an appropriate stress value for fatigue analysis of a sharp corner is commonly in terms of linearly extrapolating finite element calculated surface stresses from a number of plate thicknesses t away from the singularity to the corner. A simpler approach, developed for planar plates with sharp corners, assesses the stress on the basis of the dimensions of the corner. This thesis includes checks on the applicability, to more complicated 3-d geometry, of these previous recommendations for the assessment of corner singularities.Stiffened plated structures such as ships and box girder bridges, result in connection details that contain sharp internal corners. Many failures in ship structure have been found to be associated with fatigue crack propagation at the side shell connections between longitudinal and transverse structure. According to elastic stress analysis, these sharp corners are geometric singularities that have an infinite stress in the corner. A further complication of stiffened structures is that a crack may grow through intersections, e.g. of plates and stiffeners and changes of plate thickness before it causes a catastrophic structural failure. In this thesis, a new approach is developed to simplify the analysis of these issues. The singular stress contribution is, as usual, characterised by Y, the non-dimensional the stress intensity factor but within this method simplified analysis is used to calculate the Y values. The method combines a ratio of non-singular linearized ligament stresses to estimate the effect of large changes in crack length and changes in plate thickness with an empirical methods to estimate the local effect as the crack grows through a change of thickness. The method does not require an analysis of the actual singularity, so saving analysis time and, importantly, giving the engineer some feeling for the result and the possibility of a “back of the envelope” calculation for the SIF or Y. This work is based on running finite element analyses, to determine the Stress Intensity Factor and Y and using the results to test the empirical or analytical methods.The derived methods are useful both for assessment of existing structures and for design application. Comparing the results from the application of this new methodology with the FE method and existing fatigue analysis guidance, the new method is very much quicker and easier to apply. It is though less accurate than FE analysis and so is most appropriate for, (1) preliminary assessment, (2) reliability assessment where many structural and defect variations are to be considered and (3) for checking whether a more detailed analysis is producing sensible results. For design calculations often a stress concentration factor or SCF is needed that can be used with an S-N curve. The actual predicted peak stress and hence SCF will, for finite element analysis, depend on the element size and will normally increase as the element size decreases. The existing guidance on determining an appropriate stress value for fatigue analysis of a sharp corner is commonly in terms of linearly extrapolating finite element calculated surface stresses from a number of plate thicknesses t away from the singularity to the corner. A simpler approach, developed for planar plates with sharp corners, assesses the stress on the basis of the dimensions of the corner. This thesis includes checks on the applicability, to more complicated 3-d geometry, of these previous recommendations for the assessment of corner singularities