TURBOMOLE applicability

The two-center ERIs that enter the inequality [23] can be rapidly calculated. Application of the above estimate allows for elimination of large numbers of ERIs without sacrificing the accuracy of electronic properties. The estimate [23] is incorporated in the TURBOMOLE system of programs . 

The main goal of the present work is to report the implementation of the explicitly-correlated coupled-cluster singles-and-doubles method (CCSD(F12)) in Turbomole. This tool is capable of very efficient calculating the CCSD energies at the basis set limit with relatively small orbital basis sets. The implementation works with RHF, UHF and ROHF reference wave functions, which means that it can treat both closed- and open-shell species. The formulation in terms of intermediate quantities and the application of density fitting techniques make this implementation quite unique. 

The thesis begins with Section 2, where a brief history about the explicitly correlated approaches is presented. This is followed by Section 3 with general remarks about standard and explicitly correlated coupled-cluster theories. In Section 4, the details about the CCSD(F12) model relevant to the implementation in TuRBOMOLE are presented. The usefulness of the developed tool is illustrated with the application to the problems that are of interest to general chemistry. A very accurate determination of the reactions barrier heights of two CH3+CH4 reactions has been carried out (Section 5) and the atomization energies of 106 medium-size and small molecules were computed and compared with available experimental thermochemical data (Section 6). The ionization potentials and electron affinities of the atoms H, C, N, O and F were obtained and an agreement with the experimental values of the order of a fraction of a meV was reached (Section 7). Within all applications, the CCSD(F12) calculation was only a part of the whole computational procedure. The contributions from various levels of theory were taken into account to provide the final result, that could be successfully compared to the experiment. 

Similar to the MP2-E12 formalism, the strong orthogonality projector in the geminal basis leads to many-electron integrals in the amplitude equations. Explicit evaluation of these integrals severely restricts the range of application and the successful approaches are thc e that involve two-electron integration at most. The implementation of the CCSD(F12) in Turbomole fulfills this requirement. 

The CCSD(F12) model as well as the full CCSD-F12 approach and other simplifications of it are currently being implemented in various quantum chemistry programs [59, 61, 62, 71, 72, 73, 74, 75, 76, 77, 78, 79], also in combination with connected triples and higher excitations. In particular Kohn and co-workers [72] have shown that the CCSD(F12) model is an excellent approximation to the full CCSD-F12 approach, and the CCSD(F12) model is the method of choice that we have implemented in the Turbomole program. The present work reports on one of the first applications of CCSD(F12) theory" with chemical relevance. In such a real-life application, CCSD(F12) calculations are combined with a series of other coupled-cluster calculations including geometry optimizations, calculations of harmonic vibrational frequencies, and coupled-cluster calculations with connected triples and quadruples. Within the whole set of calculations that must be performed, the CCSD(F12) calculations take only a fraction of the total computation time, and therefore, in an application as the one presented here, there appears to be no need to further simplify the CCSD(F12) model. 

Implementation and Application of the Explicitly Correlated Coupled-Cluster Method in Turbomole... 

Implementation and application of the explicitly correlated coupled-cluster method in TURBOMOLE... 

W i) is an integral operator with kernel W p, p ) and V p, p ) is the Fourier-transformed external potential. Hess s code has been implemented in several program codes like TURBOMOLE or MOLCAS3. Most of the applications are carried out scalar (one-component) without spin-orbit coupling and usually the two-electron operator is chosen as the simple Coulomb operator. This scheme (extended to spin-orbit coupling it necessary) leads to very accurate molecular properties for even the heaviest elements. A large number of applications in the chemistry of heavy elements are carried out by using either the scalar relativistic pseudopotential or density functional approximations. The pseudopotentials most widely used are linear... 

Large-scale applications are facilitated by special features of TURBOMOLE ... 

The accurate prediction of molecular properties is the main objective of quantum chemistry. The aim is here to partially replace, to verify or to interpret measurements which are difficult or veiy expensive to carry out. The crucial problem in a theoretical treatment is the electronic Schrdclinger equation which ha.s to be solved with sufficient accuracy. A variety of methods and approximations are available for this purpose, and the method of choice depends on the actual problem types of molecules and atoms involved, electronic state, property of interest, and the required accuracy in connection with the computational resources available. TURBOMOLE supports SCF, DFT, and MP2 treatments, in various technical variants, which are at present the standard ab initio methods applicable to molecules larger than about 20 atoms plus hydrogens. For a more precise description of the functionality we list molecular properties of interest and specify the methods implemented for their computation in the present version 4.0, and in the next release, 4.1. 

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