We discuss in this review recent progress, especially by our group, on linear scaling algorithms for electronic structure calculations with numerical atomic basis sets. The principles of the construction of numerical ...
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We discuss in this review recent progress, especially by our group, on linear scaling algorithms for electronic structure calculations with numerical atomic basis sets. The principles of the construction of numerical basis sets and the Hamiltonian are introduced first. Then we discuss how to solve the single-electron equation self-consistently, and how to obtain electronic properties via post-self-consistent-field processes in a linear scaling way. The linear response calculation with linear scaling is also introduced. Numerical implementation is emphasized, with some applications presented for demonstration purposes.
In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometr...
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In many interesting semi-infinite programming problems, all the constraints are linear inequalities whose coefficients are analytical functions of a one-dimensional parameter. This paper shows that significant geometrical information on the feasible set of these problems can be obtained directly from the given coefficient functions. One of these geometrical properties gives rise to a general purification scheme for linear semi-infinite programs equipped with so-called analytical constraint systems. It is also shown that the solution sets of such kind of consistent systems form a transition class between polyhedral convex sets and closed convex sets in the Euclidean space of the unknowns.
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