Joop H. van Lenthe

Accuracy of the Boys and Bernardi function counterpoise method

The performance of the Boys and Bernardi function counterpoise (FCP) method in eliminating the basis set superposition error (BSSE) is studied for He2, at R=5.6 a.u., within the supermolecular coupled electron pair approximation (CEPA‐1) method. A series of one‐electron Gaussian basis sets is designed that allows a systematic approach to the basis set limit value of the interaction energy. Every basis set contains a part suitable to reproduce the atomic correlation energy and a second part optimized for the dispersion interaction in He2. BSSE‐free correlated first‐order interaction energies [E(1)], calculated using perturbation theory, are reported for each of these sets. Extrapolation to the basis set limit yields a new value of 33.60±0.02 μH for E(1) at R=5.6 a.u. Extending previous work, the supermolecular CEPA‐1 interaction energies for each set are then compared to the total of E(1) and the BSSE‐free Mo/ller–Plesset second‐order dispersion energy reported previously. While for some basis sets the unc...

Compact valence bond functions with breathing orbitals: Application to the bond dissociation energies of F2 and FH

An original computational method of ab initio valence bond type is proposed, aiming at yielding accurate dissociation energy curves, while dealing with wave functions being very compact and clearly interpretable in terms of Lewis structures. The basic principle is that the wave function is allowed to have different orbitals for different valence bond structures. Thus, throughout the dissociation process, the so‐called ‘‘breathing orbitals’’ follow the instantaneous charge fluctuations of the bond being broken by undergoing changes in size, hybridization, and polarization. The method is applied to the dissociation of F2 and FH. For each molecule, a wave function involving only three valence bond configurations yields equilibrium bond lengths within 0.01 A, and dissociation energies within about 2 kcal/mol of the results of estimated or true full configuration interaction in the same basis sets. The effect of dynamical electron correlation on calculated dissociation energies is analyzed. It is shown that re...

The impact of higher polarization functions of second-order dispersion energy. Partial wave expansion and damping phenomenon for He2☆

Abstract Convergence properties of the Moller—Plesset dispersion energy with respect to saturation of polarization basis set have been investigated, by means of the partial wave expansion through “i” terms, for the He dimer. The expansion proved to be slowly convergent and ineffective if accurate calculations are aimed at. The damping functions for individual terms have been evaluated and shown to be in good agreement with the semi-empirical ones. The basis set extension effect, occurring when occupied and virtual orbitals of monomers are evaluated with the basis set of a whole dimer, has been found to improve upon the slow convergence of the partial wave expansion. Additional improvement is observed on adding bond-centered functions.

Benchmark full configuration interaction calculations on the helium dimer

Full configuration interaction calculations are presented for the helium dimer employing large basis sets. Using the best basis, which contains up to h‐type basis functions and several closely spaced sets of bond functions, the interaction energy was calculated for a variety of internuclear distances in the range 4.0 to 12.0 bohr. The best calculated values for the He2 interaction energy are −10.947 K at 5.6 bohr (the van der Waals minimum) and +294.90 K at 4.0 bohr (on the repulsive wall). The interaction energy at 4.0 bohr differs significantly from the most recent semiempirical potential of Aziz and Slaman [J. Chem. Phys. 94, 8047 (1991)], indicating that this potential is too attractive around 4.0 bohr. Using a more generally accessible basis, containing only up to f‐type basis functions and only one set of bond functions, the interaction energy was calculated to be −10.903 K at 5.6 bohr and +294.96 K at 4.0 bohr. These results show that functions of higher than f symmetry and bond functions distribut...

ON THE EVALUATION OF NON-ORTHOGONAL MATRIX ELEMENTS

Abstract Lowdins formula for non-orthogonal matrix elements is derived and elucidated. Algorithms for cofactor evaluation are discussed. It is shown that for matrix elements involving two-electron operators the effort associated with the computation of the cofactors is only about three floating point operations per cofactor. We conclude that the non-orthogonality problem does not reside in the evaluation of the cofactors and that in situ generation is a viable approach. Explicit algorithms are given.

N‐Acetylmethionine and Biotin as Photocleavable Protective Groups for Ruthenium Polypyridyl Complexes

Over the last decades the large therapeutic success of cisplatin-like anticancer drugs, combined to its recognized limitations (such as acquired resistance and general toxicity), have stimulated the scientific community to find other metal-based drugs with anticancer properties. Ruthenium-based molecules, and among them those containing polypyridyl ligands, have emerged as a vast family of active compounds. However, clinical studies have shown that general toxicity remains an important issue, and ruthenium-based chemotherapy is still a heavy burden for the cancer patient. Although several mechanisms might explain their anticancer properties in vivo, the thermal aquation of ruthenium–chloride bonds, followed by coordination to DNA 16–18] and/or proteins is, like for platinum-based anticancer drugs, a highly plausible mode of action (see Figure 1, route 1). 21] However, as thermal breaking of Ru!Cl bonds in aqueous solution might happen anywhere in a human body, this mechanism is thought to be the basis of both antitumor activity and general toxicity. Our analysis that the Ru!Cl coordination bond is too weak to provide good selectivity towards cancer cells, led us to look for protective groups, that is, ligands that would hold more strongly to ruthenium than chlorides, but that could also be cleaved in a controlled way in vivo. In the ideal case, such ligands would avoid the formation of aqua complexes, and thus prevent the coordination of competing biological ligands in vivo. Thioether ligands are ideal candidates because ruthenium(II) likes binding to their soft sulfur atom. Secondly, unlike nitrogen-based ligands, thioethers are only weakly basic in water, which might make their ruthenium complexes less sensitive to pH changes. Finally, visible-light irradiation leads to the controlled release of thioether ligands, which feature might be used to deliver locally the cytotoxic form of the ruthenium complex at the desired location (Figure 1, route 2). The use of light to cure cancer, which has notably led to the clinical development of photodynamic therapy, has also been proposed as an interesting development in metal-based anticancer drug research, in which the presence of oxygen is not required. To investigate this concept, we selected two monodentate thioether ligands of natural origin: N-acetyl-l-methionine and d-biotin, and synthesized their ruthenium complexes [Ru ACHTUNGTRENNUNG(terpy) ACHTUNGTRENNUNG(bpy)(N-acetyl-l-methionine)]Cl2 (compound [3]Cl2) and [RuACHTUNGTRENNUNG(terpy)ACHTUNGTRENNUNG(bpy) ACHTUNGTRENNUNG(d-biotin)]Cl2 (compound [4]Cl2, see Scheme 1). The synthesis is straightforward: it does not require any silver salts to remove the chloride anions, but simply requires mixing in water, at 80 8C and in the dark, the chlorido complex [Ru ACHTUNGTRENNUNG(terpy) ACHTUNGTRENNUNG(bpy)Cl]Cl (compound[1]Cl, see Scheme 1) and one equivalent of the thioether ligand. The course of the reaction can be nicely monitored using H NMR spectroscopy, since each different ruthenium species present in solution gives a distinct A6 [a] R. E. Goldbach, I. Rodriguez-Garcia, S. Bonnet Leiden Institute of Chemistry, Gorlaeus Laboratories Leiden University, P.O. Box 9502 2300 RA Leiden (The Netherlands) E-mail : bonnet@chem.leidenuniv.nl [b] J. H. v. Lenthe Theoretical Chemistry Group Debye Institute for Nanomaterial Science Faculty of Science, Utrecht University Padualaan 8, 3584 CH Utrecht (The Netherlands) [c] M. A. Siegler Small Molecule X-ray Facility Department of Chemistry, Johns Hopkins University Baltimore, MD 21218 (USA) Supporting information for this article (including synthetic procedures, full characterization and high-resolution ES-MS spectra of complexes [3]Cl2 and [4]Cl2; notations for the assignments of the NMR spectra and H NMR spectra; X-ray crystallography resolution method and data; ferrioxalate actinometry, quantum yield measurement procedures, H NMR and kinetic data for irradiation experiments; calculation procedure and x,y,z coordinates for the DFT-minimized species [3A] , [3B] , [4A], and [4B]) is available on the WWW under http://dx.doi.org/10.1002/chem.201101541. Figure 1. One of the modes of action of ruthenium polypyridyl anticancer drugs (reaction 1), and a new photochemotherapy strategy using analogous complexes “protected” by thioethers ligands and “deprotected” by visible light irradiation (reaction 2).

Software news and updates

A parallel version of the valence bond program TURTLE has been developed. In this version the calculation of matrix elements is distributed over the processors. The implementation has been done using the message‐passing interface (MPI), and is, therefore, portable. The parallel version of the program is shown to be quite efficient with a speed‐up of 55 at 64 processors.

Gradients in valence bond theory

A gradient method for general valence bond wave functions is presented. The electronic energy is used as a Lagrange multiplier. The derivatives of the normalization and of the first- and second-order cofactors present in the energy expression have to be evaluated, giving rise to first-, second-, and third-order cofactors. This evaluation is done using an extension of methods described previously. The use of gradients is illustrated with some calculations on organic molecules, viz. ethene, 1, 4-butadiene, and benzene.

The size consistency of multi-reference Møller–Plesset perturbation theory

The size consistency of multi-reference Moller–Plesset perturbation theory as a function of the structure of the zeroth-order Hamiltonian is studied. In calculations it is shown that the choice of projection operators to define the zeroth-order Hamiltonian is crucial. In essence whenever such a projection operator can be written as the sum of projection operators onto particular subspaces, cross-product terms may appear in the zeroth-order Hamiltonian that spoil the size consistency. This problem may be solved using a separate projection operator for each subspace spanning an excitation level. In principle a zeroth-order Hamiltonian based on these projection operators results in a size consistent perturbation theory. However, it was found that some non-local spin recoupling effects remain. A new zeroth-order Hamiltonian formulated recently circumvents this problem and is shown to be exactly size consistent. Apart from the choice of projection operators, the orthogonalization of the excited states is cruci...

An improved ab initio relativistic zeroth-order regular approximation correct to order 1/c2

The equations of the original ab initio scalar-relativistic zeroth-order regular approximation (ZORA) and the infinite-order regular approximation (IORA) are expanded in orders of 1/c2. It is shown that previous ZORA/IORA implementations in ab initio quantum chemistry programs were not correct to order 1/c2, but contained imperfections leading to fictitious self-interactions. These errors can be avoided by adding exchange-type terms (coupling the large and small components) to the relativistic ZORA correction to the Hamiltonian, yielding improved ab initio relativistic zeroth- and infinite-order regular approximations that are correct to order 1/c2. The new methods have been tested numerically by computing the total energies, orbital energies, and static electric dipole polarizabilities of the rare gas atoms He through Xe.