{"product_id":"gradients-and-non-adiabatic-derivative-coupling-terms-for-spin-orbit-wavefunctions-9781288315710","title":"Gradients and Non-Adiabatic Derivative Coupling Terms for Spin-Orbit Wavefunctions","description":"\u003cp\u003e • Author(s): Lachlan T. Belcher\u003cbr\u003e • Publisher: Biblioscholar\u003cbr\u003e • Publisher Imprint: Biblioscholar\u003cbr\u003e • BISAC: General\u003c\/p\u003e\u003cp\u003eAnalytic gradients of electronic eigenvalues require one calculation per nuclear geometry, compared to 3n calculations for finite difference methods, where n is the number of nuclei. Analytic non-adiabatic derivative coupling terms, which are calculated in a similar fashion, are used to remove non-diagonal contributions to the kinetic energy operator, leading to more accurate nuclear dynamics calculations than those that employ the Born-Oppenheimer approximation and assume off-diagonal contributions are zero. The current methods and underpinnings for calculating both of these quantities for MRCI-SD wavefunctions in COLUMBUS are reviewed. Before this work, these methods were not available for wavefunctions of a relativistic MRCI-SD Hamiltonian. A formalism for calculating the density matrices, analytic gradients, and analytic derivative coupling terms for those wavefunctions is presented. The results of a sample calculation using a Stuttgart basis for K He are presented.\u003c\/p\u003e","brand":"Biblioscholar","offers":[{"title":"Paperback","offer_id":46862434533527,"sku":"9781288315710","price":5141.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9781288315710.webp?v=1769966187","url":"https:\/\/atlanticbooks.com\/products\/gradients-and-non-adiabatic-derivative-coupling-terms-for-spin-orbit-wavefunctions-9781288315710","provider":"Atlantic Books","version":"1.0","type":"link"}