{"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":"Analytic 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Lachlan T. Belcher\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Biblioscholar\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/19\/2012\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 230\u003cbr\u003e\u003cb\u003eBinding Type:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 0.92lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.69h x 7.44w x 0.48d\u003cbr\u003e\u003cb\u003eISBN:\u003c\/b\u003e 9781288315710\u003cp\u003e\u003ci\u003eThis title is not returnable\u003c\/i\u003e\u003cbr\u003e\u003c\/p\u003e","brand":"Biblioscholar","offers":[{"title":"Paperback","offer_id":44176494166131,"sku":"9.78129E+12","price":87.47,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0555\/9255\/0515\/files\/img_abc2cb93-d13f-49a2-b2d1-aa52d3af2d53.jpg?v=1766580922","url":"https:\/\/bookstorenmore.com\/products\/gradients-and-non-adiabatic-derivative-coupling-terms-for-spin-orbit-wavefunctions-9781288315710","provider":"Bookstore N More","version":"1.0","type":"link"}