Kristine Pierloot

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions

SummaryGenerally contracted basis sets for second row atoms have been constructed using the Atomic Natural Orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over several atomic states, positive and negative ions, and atoms in an external electric field. The contracted basis sets give virtually identical results as the corresponding uncontracted sets for the atomic properties, which they have been designed to reproduce. The design objective has been to describe the ionization potential, the electron affinity, and the polarizability as accurately as possible. The result is a set of well balanced basis sets for molecular calculations. The starting primitive sets are 17s12p5d4f for the second row atoms Na-Ar. Corresponding ANO basis sets for first row atoms have recently been published.

Density matrix averaged atomic natural orbital (ANO) basis sets for correlated molecular wave functions: IV. Medium size basis sets for the atoms H-Kr

SummaryGenerally contracted Basis sets for the atoms H-Kr have been constructed using the atomic natural orbital (ANO) approach, with modifications for allowing symmetry breaking and state averaging. The ANOs are constructed by averaging over the most significant electronic states, the ground state of the cation, the ground state of the anion for some atoms and the homonuclear diatomic molecule at equilibrium distance for some atoms. The contracted basis sets yield excellent results for properties of molecules such as bond-strengths and-lengths, vibrational frequencies, and good results for valence spectra, ionization potentials and electron affinities of the atoms, considering the small size of these sets. The basis sets presented in this article constitute a balanced sequence of basis sets suitable for larger systems, where economy in basis set size is of importance.

The restricted active space followed by second-order perturbation theory method: Theory and application to the study of CuO2 and Cu2O2 systems

A multireference second-order perturbation theory using a restricted active space self-consistent field wave function as reference (RASPT2/RASSCF) is described. This model is particularly effective for cases where a chemical system requires a balanced orbital active space that is too large to be addressed by the complete active space self-consistent field model with or without second-order perturbation theory (CASPT2 or CASSCF, respectively). Rather than permitting all possible electronic configurations of the electrons in the active space to appear in the reference wave function, certain orbitals are sequestered into two subspaces that permit a maximum number of occupations or holes, respectively, in any given configuration, thereby reducing the total number of possible configurations. Subsequent second-order perturbation theory captures additional dynamical correlation effects. Applications of the theory to the electronic structure of complexes involved in the activation of molecular oxygen by mono- and binuclear copper complexes are presented. In the mononuclear case, RASPT2 and CASPT2 provide very similar results. In the binuclear cases, however, only RASPT2 proves quantitatively useful, owing to the very large size of the necessary active space.

Applications of level shift corrected perturbation theory in electronic spectroscopy

Abstract Multiconfigurational second-order perturbation theory (CASPT2) with a level shift technique used to reduce the effect of intruder states has been tested for applications in electronic spectroscopy. The following molecules have been studied: formamide, adenine, stilbene, Ni(CO) 4 , and a model compound for the active site in the blue copper protein plastocyanin, Cu(Im) 2 (SH)(SH 2 ) + . The results show that the level shift technique can be used to remove the effects of the intruder states in all these molecules. In some cases a drift in the energies as a function of the level shift is observed, which however is small enough that the normal error bar for CASPT2 excitation energies (≈ 0.3 eV ) still holds.

The CASPT2 method in inorganic electronic spectroscopy: from ionic transition metal to covalent actinide complexes

During the past ten years, the CASSCF/CASPT2 method has been applied with considerable success to a substantial number of problems related to the electronic spectroscopy of transition metal complexes, thus providing a definite breakthrough of ab initio quantum chemistry in this domain. This will be illustrated in the present contribution by means of a few representative cases from the field of inorganic, organometallic and bio-chemistry. Furthermore, CASPT2 results obtained for the excitation energies of the ions UO2 2+ and UO2Cl4 2- will be presented, indicating that the method is also applicable with comparable accuracy for molecules with very heavy metals (provided that relativistic effects are accounted for). We will also show that the success of the method is critically dependent upon its judicious application, in particular upon the choice of the orbitals to be included in the reference active space. A link will be made between the latter choice and the specific electronic structure of the metal—ligand interactions.

Electronic Structure of Selected {FeNO}7 Complexes in Heme and Non-Heme Architectures: A Density Functional and Multireference ab Initio Study

The multiconfigurational CASSCF/CASPT2 approach, along with various functionals of density functional theory, is applied to selected iron(II)-nitrosyl ({FeNO}(7)) complexes, both with heme and nonheme groups. The energetics of the lowest doublet and quartet spin states at the correlated ab initio (CASPT2) level is presented for the first time. Comparison of the CASSCF and (unrestricted) DFT spin densities indicates that the nonhybrid functionals yield the spin densities most closely to the ab initio ones. The analysis of the multiconfigurational CASSCF wave function in terms of the localized active orbitals allows one to resolve the nature of Fe-NO bonding as a mixture of Fe(II)-NO(0) and Fe(III)-NO(-) resonance structures (in comparable contributions) for both spin states and various ligands.

Multiconfigurational Second-Order Perturbation Theory Restricted Active Space (RASPT2) Method for Electronic Excited States: A Benchmark Study

The recently developed second-order perturbation theory restricted active space (RASPT2) method has been benchmarked versus the well-established complete active space (CASPT2) approach. Vertical excitation energies for valence and Rydberg excited states of different groups of organic (polyenes, acenes, heterocycles, azabenzenes, nucleobases, and free base porphin) and inorganic (nickel atom and copper tetrachloride dianion) molecules have been computed at the RASPT2 and multistate (MS) RASPT2 levels using different reference spaces and compared with CASPT2, CCSD, and experimental data in order to set the accuracy of the approach, which extends the applicability of multiconfigurational perturbation theory to much larger and complex systems than previously. Relevant aspects in multiconfigurational excited state quantum chemistry such as the valence-Rydberg mixing problem in organic molecules or the double d-shell effect for first-row transition metals have also been addressed.

Performance of CASPT2 and DFT for Relative Spin-State Energetics of Heme Models

The accuracy of the relative spin-state energetics of three small Fe(II) or Fe(III) heme models from multiconfigurational perturbation theory (CASPT2) and density functional theory with selected functionals (including the recently developed M06 and M06-L functionals) was assessed by comparing with recently available coupled cluster results. While the CASPT2 calculations of spin-state energetics were found to be very accurate for the studied Fe(III) complexes (including FeP(SH), a model of the active site of cytochrome P450 in its resting state), there is a strong indication of a systematic error (around 5 kcal/mol) in favor of the high-spin state for the studied Fe(II) complexes (including FeP(Im), a model of the active site of myoglobin). A larger overstabilization of the high-spin states was observed for the M06 and M06-L functionals, up to 22 and 11 kcal/mol, respectively. None of the tested density functionals consistently provides a better accuracy than CASPT2 for all model complexes.

Electronic structure and spectrum of UO22+ and UO2Cl42−

A theoretical study is presented of the electronic spectra of the UO(2) (2+) and UO(2)Cl(4) (2-) ions, based on multiconfigurational perturbation theory (CASSCF/CASPT2), combined with a recently developed method to treat spin-orbit coupling [P.-A. Malmqvist et al., Chem. Phys. Lett. 357, 230 (2002); B. O. Roos and P.-A. Malmqvist, Phys. Chem. Chem. Phys. 6, 2919 (2004)]. The results are compared to the experimental spectroscopic data obtained for uranyl ions in Cs(2)UO(2)Cl(4) crystals from Denning [Struct. Bonding (Berlin) 79, 215 (1992)] and to previous theoretical calculations performed using a combined configuration-interaction spin-orbit treatment [Z. Zhang and R. M. Pitzer, J. Phys. Chem. A 103, 6880 (1999); S. Matsika and R. M. Pitzer, J. Phys. Chem. A. 105, 637 (2001)]. As opposed to the latter results, the calculations performed in this work point to a significant effect of the weakly bound equatorial chlorine ligands on the excitation energies.

A THEORETICAL STUDY OF THE CHEMICAL BONDING IN M(CO)X (M=CR, FE, AND NI)

The equilibrium structure and bond energies of the transition metal complexes Ni(CO)x (x=1–4), Fe(CO)5, and Cr(CO)6 have been studied using the complete active space (CAS)SCF method and second‐order perturbation theory (CASPT2). It is shown that the major features of the electronic structure are properly described by a CASSCF wave function based on an active space comprising the bonding and antibonding orbitals directly involved in the metal–ligand bond. Remaining correlation effects are dealt with in the second, CASPT2, step. The computed energies have been corrected for basis set superposition errors (BSSE) and relativistic corrections have been added. Resulting bond distances and bond energies are in agreement with experimental data, when available: Cr(CO)6, r(Cr–C)=1.91(1.91) A, D0=148(153) kcal/mol; Fe(CO)5, rax(Fe–C) =1.79(1.81) A, req(Fe–C)=1.80(1.83) A, D0=133(137) kcal/mol; Ni(CO)4, r(Ni–C)=1.83(1.83) A, D0=139(138) kcal/mol (experimental values within parentheses). Some excited states were compu...