Florian Weigend

RI-MP2 : OPTIMIZED AUXILIARY BASIS SETS AND DEMONSTRATION OF EFFICIENCY

Abstract Applications of the RI-MP2 method require high-quality auxiliary basis sets employed to approximate charge distributions. A variational procedure is proposed and applied to optimize auxiliary bases for main group and transition metal atoms which are tested for more than 350 molecules. The RI approximation affects molecular MP2 energies by less than 60 μ E h per atom and equilibrium distances by less than 0.2 pm. We further comment on the extension from RHF to UHF and the exploitation of molecular symmetry. Applications to (Cu 2 S) n clusters and hydrocarbons C n H 2 n +2 document a significant reduction of computation times which allows for calculations with up to 1000 basis functions in C 1 symmetry.

Accurate Coulomb-fitting basis sets for H to Rn.

A series of auxiliary basis sets to fit Coulomb potentials for the elements H to Rn (except lanthanides) is presented. For each element only one auxiliary basis set is needed to approximate Coulomb energies in conjunction with orbital basis sets of split valence, triple zeta valence and quadruple zeta valence quality with errors of typically below ca. 0.15 kJ mol(-1) per atom; this was demonstrated in conjunction with the recently developed orbital basis sets of types def2-SV(P), def2-TZVP and def2-QZVPP for a large set of small molecules representing (nearly) each element in all of its common oxidation states. These auxiliary bases are slightly more than three times larger than orbital bases of split valence quality. Compared to non-approximated treatments, computation times for the Coulomb part are reduced by a factor of ca. 8 for def2-SV(P) orbital bases, ca. 25 for def2-TZVP and ca. 100 for def2-QZVPP orbital bases.

Efficient use of the correlation consistent basis sets in resolution of the identity MP2 calculations

The convergence of the second-order Moller–Plesset perturbation theory (MP2) correlation energy with the cardinal number X is investigated for the correlation consistent basis-set series cc-pVXZ and cc-pV(X+d)Z. For the aug-cc-pVXZ and aug-cc-pV(X+d)Z series the convergence of the MP2 correlation contribution to the dipole moment is studied. It is found that, when d-shell electrons cannot be frozen, the cc-pVXZ and aug-cc-pVXZ basis sets converge much slower for third-row elements then they do for first- and second-row elements. Based on the results of these studies criteria are deduced for the accuracy of auxiliary basis sets used in the resolution of the identity (RI) approximation for electron repulsion integrals. Optimized auxiliary basis sets for RI-MP2 calculations fulfilling these criteria are reported for the sets cc-pVXZ, cc-pV(X+d)Z, aug-cc-pVXZ, and aug-cc-pV(X+d)Z with X=D, T, and Q. For all basis sets the RI error in the MP2 correlation energy is more than two orders of magnitude smaller than...

CC2 excitation energy calculations on large molecules using the resolution of the identity approximation

A new implementation of the approximate coupled cluster singles and doubles method CC2 is reported, which is suitable for large scale integral-direct calculations. It employs the resolution of the identity (RI) approximation for two-electron integrals to reduce the CPU time needed for calculation and I/O of these integrals. We use a partitioned form of the CC2 equations which eliminates the need to store double excitation cluster amplitudes. In combination with the RI approximation this formulation of the CC2 equations leads to a reduced scaling of memory and disk space requirements with the number of correlated electrons (n) and basis functions (N) to, respectively, O(N2) and O(nN2), compared to O(n2N2) in previous implementations. The reduced CPU, memory and disk space requirements make it possible to perform CC2 calculations with accurate basis sets on large molecules, which would not be accessible with conventional implementations of the CC2 method. We present an application to vertical excitation ene...

Gaussian basis sets of quadruple zeta valence quality for atoms H-Kr

We present Gaussian basis sets of quadruple zeta valence quality with a segmented contraction scheme for atoms H to Kr. This extends earlier work on segmented contracted split valence (SV) and triple zeta valence (TZV) basis sets. Contraction coefficients and orbital exponents are fully optimized in atomic Hartree–Fock (HF) calculations. As opposed to other quadruple zeta basis sets, the basis set errors in atomic ground-state HF energies are less than 1 mEh and increase smoothly across the Periodic Table, while the number of primitives is comparably small. Polarization functions are taken partly from previous work, partly optimized in atomic MP2 calculations, and for a few cases determined at the HF level for excited atomic states nearly degenerate with the ground state. This leads to basis sets denoted QZVP for HF and density functional theory (DFT) calculations, and for some atoms to a larger basis recommended for correlated treatments, QZVPP. We assess the performance of the basis sets in molecular HF...

A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency

A direct HF algorithm using the resolution of identity for Coulomb and exchange integrals (RI-HF) was implemented within the program system TURBOMOLE. A variational procedure for the optimisation of auxiliary functions is presented as well as optimised auxiliary basis sets for large basis sets up to Br. The accuracy of RI-HF energies and of MP2 energies based on RI-HF wave functions is demonstrated for a large test set of molecules. Accuracy of first order properties is documented for selected cases. The size dependency of the RI errors and the efficiency of the method are investigated for closo-boranes [BnHn]2− (n = 4–12).

Hartree–Fock exchange fitting basis sets for H to Rn †

For elements H to Rn (except Lanthanides), a series of auxiliary basis sets fitting exchange and also Coulomb potentials in Hartree–Fock treatments (RI‐JK‐HF) is presented. A large set of small molecules representing nearly each element in all its common oxidation states was used to assess the quality of these auxiliary bases. For orbital basis sets of triple zeta valence and quadruple zeta valence quality, errors in total energies arising from the RI‐JK approximation are below ∼1 meV per atom in molecular compounds. Accuracy of RI‐JK‐approximated HF wave functions is sufficient for being used for post‐HF treatments like Møller–Plesset perturbation theory, MP2. Compared to nonapproximated treatments, RI‐JK‐HF leads to large computational savings for quadruple zeta valence orbital bases and, in case of small to midsize systems, to significant savings for triple zeta valence bases.

Electronic transport through single conjugated molecules

Abstract We investigate electronic transport through single conjugated molecules, and compare our data to results of quantum chemical calculations. Conductance spectra of two types of molecules are studied in a metal–molecule–metal junction established using the mechanically controlled break-junction technique. We observe a suppressed conductance at low bias, characteristic step-like features at higher voltages, and strong sample-to-sample fluctuations. We develop a quantum-chemical model for our system using DFT calculations, with the electrodes modelled by small clusters. We consider the effects of different geometries of molecule–metal configurations and bonding as well as finite electric field, and are thereby able to account for the phenomenology of the experimental data.

Self-consistent treatment of spin–orbit interactions with efficient Hartree–Fock and density functional methods

Efficient self-consistent field (SCF) schemes including both scalar relativistic effects and spin-orbit (SO) interactions at Hartree-Fock (HF) and density functional (DFT) levels are presented. SO interactions require the extension of standard procedures to two-component formalisms. Efficiency is achieved by using effective core potentials (ECPs) and by employing the resolution-of-the-identity approximation for the Coulomb part (RI-J) in pure DFT calculations as well as also for the HF-exchange part (RI-JK) in the case of HF or hybrid-DFT treatments. The procedures were implemented in the program system TURBOMOLE; efficiency is demonstrated for comparably large systems, such as Pb54. Relevance of SO effects for electronic structure and stability is illustrated by treatments of small Pb and Po clusters with and without accounting for SO effects.

Slow magnetic relaxation in trigonal-planar mononuclear Fe(II) and Co(II) bis(trimethylsilyl)amido complexes. A comparative study

Alternating current magnetic investigations on the trigonal-planar high-spin Co(2+) complexes [Li(15-crown-5)] [Co{N(SiMe3)2}3], [Co{N(SiMe3)2}2(THF)] (THF = tetrahydrofuran), and [Co{N(SiMe3)2}2(PCy3)] (Cy = -C6H13 = cyclohexyl) reveal that all three complexes display slow magnetic relaxation at temperatures below 8 K under applied dc (direct current) fields. The parameters characteristic for their respective relaxation processes such as effective energy barriers Ueff (16.1(2), 17.1(3), and 19.1(7) cm(-1)) and relaxation times τ0 (3.5(3) × 10(-7), 9.3(8) × 10(-8), and 3.0(8) × 10(-7) s) are almost the same, despite distinct differences in the ligand properties. In contrast, the isostructural high-spin Fe(2+) complexes [Li(15-crown-5)] [Fe{N(SiMe3)2}3] and [Fe{N(SiMe3)2}2(THF)] do not show slow relaxation of the magnetization under similar conditions, whereas the phosphine complex [Fe{N(SiMe3)2}2(PCy3)] does, as recently reported by Lin et al. (Lin, P.-H.; Smythe, N. C.; Gorelsky, S. I.; Maguire, S.; Henson, N. J.; Korobkov, I.; Scott, B. L.; Gordon, J. C.; Baker, R. T.; Murugesu, M. J. Am. Chem. Soc. 2011, 135, 15806.) Distinctly differing axial anisotropy D parameters were obtained from fits of the dc magnetic data for both sets of complexes. According to density functional theory (DFT) calculations, all complexes possess spatially nondegenerate ground states. Thus distinct spin-orbit coupling effects, as a main source of magnetic anisotropy, can only be generated by mixing with excited states. This is in line with significant contributions of excited determinants for some of the compounds in complete active space self-consistent field (CASSCF) calculations done for model complexes. Furthermore, the calculated energetic sequence of d orbitals for the cobalt compounds as well as for [Fe{N(SiMe3)2}2(PCy3)] differs significantly from the prediction by crystal field theory. Experimental and calculated (time-dependent DFT) optical spectra display characteristic d-d transitions in the visible to near-infrared region. Energies for lowest transitions range from 0.19 to 0.35 eV; whereas, for [Li(15-crown-5)][Fe{N(SiMe3)2}3] a higher value is found (0.66 eV). Zero-field (57)Fe Mößbauer spectra of the three high-spin iron complexes exhibit a doublet at 3 K with small and similar values of the isomer shifts (δ), ranging between 0.57 and 0.59 mm/s, as well as an unusual small quadrupole splitting (ΔEQ = 0.60 mm/s) in [Li(15-crown-5)][Fe{N(SiMe3)2}3].