Applications of effective core potentials and density functional theory to the spin states of iron porphyrin

We investigated the performance of the B3LYP density functional in combination with ab initio effective core potentials (ECPs) that are derived from either Hartree-Fock or Dirac-Fock calculations. The transferability of ab initio ECPs is assessed on the basis of comparison with all-electron density functional calculations. For iron(II) porphyrin in particular, our assessment focused on the relative energetic ordering of five low-lying spin states, 1A1G, 3A1G, 3B2G, 5A2G, and 5B1G, and their properties, including optimized structures, charge distribution, spin density, and vibrational frequencies. Our results show that core electron correlation and core-valence electron correlation do not have significant effects on the relative energetics of the spin states of iron porphyrin. Our calculations suggest that effects of replacing the core electrons with ECPs are less significant than the choice of basis functions. We conclude that ab initio ECPs such as LANL2, RCEP, and MEFIT-R may be combined with the B3LYP density functional theory to provide consistent and accurate results.     

Ab initio calculations on some transition metal heptoxides by using effective core potentials

The ab initio molecular structures and vibrational frequencies for several transition metal heptoxides X₂O₇ⁿ⁻ (n=0, 2, 4) were calculated using effective core potentials at the HF and DFT (B3LYP) levels. The relative merits of different valence basis set arrangements were tested by comparison with experimental results available, in particular with gas-phase Re₂O₇ molecular structure and vibrational frequencies. The calculations were then extended to other heptoxides of the VB, VIB and VIIB transition metal groups. The results indicate that a staggered geometry (either D_3d or C₂) is the energy minimum for most of the heptoxides studied. The only exceptions are Mn₂O₇, which clearly prefers an eclipsed C_2v(syn) configuration, and Tc₂O₇, for which C₂ and C_2v(syn) geometries have nearly the same energy.

Particular attention was given to the magnitude of the X–O–X bond angle, as this structural parameter has been a matter of some controversy. The calculated values range from 125° (Mn₂O₇) to 180° (Group VB heptoxides) and depend on the position of the transition metal in the Periodic Table. A tendency for linearity of the X–O–X moiety on going both downwards the group and backwards the period was observed and discussed.     

Core distortions in metal atoms and the use of effective core potentials

The recent experimental determination of the geometry of Ti(CH₃)₂Cl₂ shows it to be inconsistent with the VSEPR model, a result not uncommon for molecules containing transition metal atoms. The valence shell charge concentrations (CCs) that appear as maxima in L(r)=−²ρ(r), provide a physical basis for the VSEPR model of molecular geometry for main group molecules. The same model accounts for the geometry of transition metal molecules with the proviso that the CCs are formed within the outer shell of the core of the metal atom, as defined by the shell structure of L(r). This observation appears to be in conflict with calculations for Ti(CH₃)₂Cl₂ showing that its geometry can be predicted using an effective core potential for the metal atom, a procedure that would appear to preclude the presence of core distortions. The apparent contradiction is resolved by distinguishing between the definition of the core using L(r) and one based on the orbital model.     

Utilizing relativistic effective core potentials for accurate calculations of molecular polarizabilities on transition metal compounds

The requirements necessary to extend an ECP basis set for the calculation of electric and linear optical properties to the transition metals are studied. Previously an augmentation of the SBK basis set for 39 elements with s and p electron only valences (H-Rn, excluding Ga, In, and Tl) [J. Comput. Chem., 2005, 26, 1464-1471] was presented. In this work, electric dipole moments, polarizabilities, and anisotropies of selected metal hydrides, sulfides, and bromides, cisplatin, and the Fe, Ru, and Os metallocene derivatives along with many other systems are calculated and discussed. ECP calculations of molecules containing 3d and 4d metal centers among main group atoms have good agreement, often within 1-2% of the all-electron result at the time-dependent Hartree-Fock (TDHF)/Sadlej level of theory. Molecules with a 5d metal center have a large difference from and are more accurate than the all-electron results due to the inclusion of relativistic effects in the ECPs. The polarizability as calculated with and without ECPs of metallic clusters and surfaces is increasingly different as atomic number increases, again due to a lack of relativistic effects in the all-electron calculations. The augmented ECP calculations are consistent with relativistic all-electron results, while the Sadlej calculations are consistent with other nonrelativistic results. Both relativistic and basis set effects are less noticeable when the metal is in a formally positive state.     

Fe and Ni AB initio effective potentials for use in molecular calculations

We present effective potentials to replace the Ar core electrons of Fe and Ni. These effective potentials are obtained from ab initio ground state wavefunctions of Fe and Ni and are tested by comparing with ab initio SCF calculations for excited states of Fe, Fe⁺, Fe²⁺, Fe³⁺, Ni, Ni⁺, Ni²⁺, and the FeH⁺ molecule.     

On the use of effective core potentials in the calculation of magnetic properties, such as magnetizabilites and magnetic shieldings

State-of-the art effective core potentials (ECPs) that replace electrons of inner atomic cores involve non-local potentials. If such an effective core potential is added to the Hamiltonian of a system in a magnetic field, the resulting Hamiltonian is not gauge invariant. This means, magnetic properties such as magnetisabilities and magnetic shieldings (or magnetic susceptibilities and nuclear magnetic resonance chemical shifts) calculated with different gauge origins are different even for exact solutions of the Schro?dinger equation. It is possible to restore gauge invariance of the Hamiltonian by adding magnetic field dependent terms arising from the effective core potential. Numerical calculations on atomic and diatomic model systems (potassium mono-cation and potassium dimer) clearly demonstrate that the standard effective core potential Hamiltonian violates gauge invariance, and this affects the calculation of magnetisabilities more strongly than the calculation of magnetic shieldings. The modified magnetic field dependent effective core potential Hamiltonian is gauge invariant, and therefore it is the correct starting point for distributed gauge origin methods. The formalism for gauge including atomic orbitals (GIAO) and individual gauge for localized orbitals methods is worked out. ECP GIAO results for the potassium dimer are presented. The new method performs much better than a previous ECP GIAO implementation that did not account for the non-locality of the potential. For magnetic shieldings, deviations are clearly seen, but they amount to few ppm only. For magnetisabilities, our new ECP GIAO implementation is a major improvement, as demonstrated by the comparison of all-electron and ECP results.     

Core-valence correlation potentials based on density functional theory. Applications to valence-electron-only calculations on Na and K diatomics

The core-valence correlation potential has been derived for Na and K employing atomic calculations which make use of the density functional formula worked out by Lee, Yang and Parr based on Colle-Salvetti approach. The numerical potential is fitted with a small number of Gaussians leading to a very simple expression for an one-electron corevalence correlation operator? _cv . The core-valence correlation corrections can be computed by applying? _cv on a quite general class of wavefunctions. Applications of the? _cv operator within the framework of valence-electron-only calculations using effective Hamiltonians are presented for Na and K atoms, for Na₂, K₂, NaK and their cations. Almost all the corrections calculated for the physical properties due to the core-valence correlation lead to results which are in good agreement with those obtained from much more sophisticated treatments and experimental data.     

Orbital-shell density functional in calculations on the intramolecular and intermolecular potentials for chromium atoms and benzene molecules

Calculations have been performed in the orbital-shell density-functional approximation from the nonempirical approximating quasiparticle density function, which show that the total potential energy surface for the CrBz complex is described by a two-well interaction potential. The minimum in the short-range part of the potential corresponds to an intramolecular bond in a bisarenechromium charge-transfer complex, while the minimum in the long-range part describes the molecular interaction between those components in atomically dispersed solutions of chromium in arene matrices. Good agreement with experiment is obtained.Translated from Teoreticheskaya i Éksperimental'naya Khimiya, Vol. 26, No. 2, pp. 218–220, March–April, 1990.     

Complexation of the carbonate, nitrate, and acetate anions with the uranyl dication: density functional studies with relativistic effective core potentials

The structures and vibrational frequencies of uranyl carbonates, [UO2(CO3)n](2-2n) and [(UO2)3(CO3)6]6-, uranyl nitrates, [UO2(NO3)n](2-n), and uranyl acetates, [UO2(CH3COO)n](2-n) (n = 1,2,3) have been calculated by using local density functional theory (LDFT). Only bidentate ligand coordination modes to the uranyl dication have been modeled. The calculated structures and frequencies are compared to available experimental data, including IR, Raman, X-ray diffraction, and EXAFS solution and crystal structure data. The energetics of ligand binding have been calculated using the B3LYP hybrid functional. In general, the structural and vibrational results at the LDFT level are in good agreement with experimental results and provide realistic pictures of solution phase and solid-state behavior. For the [UO2(CO3)3]6- anion, calculations suggest that complexity in the CO3(2-) stretching signature upon complexation is due to the formation of C=O and C-O domains, the latter of which can split by as much as 300 cm(-1). Assessment of the binding energies indicate that the [UO2(CO3)2]2- anion is more stable than the [UO2(CO3)3]4- anion due to the accumulation of excess charge, whereas the tri-ligand species are the most stable in the nitrate and acetate anions.     

Modeling intermolecular effects on nonlinear optical properties of transition-metal complexes. An effective core potential study

An initial effort to study the nonlinear optical (NLO) properties of interacting transition-metal-oxo complexes is presented and studied by effective core potential approaches. Osmium tetroxide is used for this study. Favorable intermolecular interaction effects, even within this weak interaction regime, that yield enhancements in NLO properties have been found. Interaction effects increase alpha (polarizability) up to 6% and gamma (second hyperpolarizability) up to 100% relative to the isolated monomer result for OsO4. The magnitude of the interaction (hyper)polarizabilities, and indeed even the sign, is found to be quite sensitive to the relative orientation of the osmium tetroxide monomers.     

Development and testing of a compact basis set for use in effective core potential calculations on rhodium complexes

We present a set of effective core potential (ECP) basis sets for rhodium atoms which are of reasonable size for use in electronic structure calculations. In these ECP basis sets, the Los Alamos ECP is used to simulate the effect of the core electrons while an optimized set of Gaussian functions, which includes polarization and diffuse functions, is used to describe the valence electrons. These basis sets were optimized to reproduce the ionization energy and electron affinity of atomic rhodium. They were also tested by computing the electronic ground state geometry and harmonic frequencies of [Rh(CO)₂μ‐Cl]₂, Rh(CO)₂ClPy, and RhCO (neutral and its positive, and negative ions) as well as the enthalpy of the reaction of [Rh(CO)₂μ‐Cl]₂ with pyridine (Py) to give Rh(CO)₂ClPy, at different levels of theory. Good agreement with experimental values was obtained. Although the number of basis functions used in our ECP basis sets is smaller than those of other ECP basis sets of comparable quality, we show that the newly developed ECP basis sets provide the flexibility and precision required to reproduce a wide range of chemical and physical properties of rhodium compounds. Therefore, we recommend the use of these compact yet accurate ECP basis sets for electronic structure calculations on molecules involving rhodium atoms. © 2012 Wiley Periodicals, Inc.     

On incorporation of atomic correlation in transition-metal molecular calculations: NiH

The atomic correlation terms necessary to lead to anaccurate 4s²3d⁸-4s^t 3d⁹ separation for the Ni atom have been incorporated into all-electron MC SCF/Cl calculations for the X² Δ state of NiH. The calculated potential curve properties are significantly improved compared to calculations which dissociate to Hartree-Fock atoms.     

Nonlocal density functional calculations of the jellium metal surface

The Becke exchange functional is used for calculation of properties of the jellium model using the slab geometry inside a box with the infinite potential barriers at the boundaries. We simplify semianalytical representation of matrix elements. We calculate the surface energies and work functions with self-consistent electron densities. For all densities (here, we give results in erg/cm² for r_s = 2.07 bohr, in comparison with the LSD approximation (?602)) and the uncorrected Pw GGA -II (?730), the Becke-II exchange only (?1212), and the Becke-II exchange with Perdew86 correlation (?830) [always close to Pw GGA -I (?814)] give smaller surface energies. The most important factor determining values of surface energies from different GGAS seems to be a form of a correlation potential. We also calculate the effect of finite slab thickness and the vacuum region thickness on the surface energy at the LSD level and indicate its importance in various jellium model calculations. © 1995 John Wiley & Sons, Inc.     

Potential energy curves for ground and excited states of NaLi from ab initio calculations with effective core polarization potentials

Sixteen low-lying electronic states of NaLi are investigated by SCF/valence Cl calculations including core polarization effects by means of an effective potential. Spectroscopic constants are obtained with estimated uncertainties of ΔR_e ? 0.01 Å, Δω_e ? 0.6 cm^?1 and ΔD_e ? 80 cm^?1. From a comparison of experimental and theoretical G(υ) values, we suggest a ground-state dissociation energy of 7093 ± 5 cm^?1. Using our rovibrational energies and recently measured excitation lines, we are able to improve the T_e values and dissociation energies of five excited states to an accuracv of ±8 cm^?1.     

Lattice match in density functional calculations: ice Ih vs. beta-AgI

Density functional optimizations of the crystal parameters of ice Ih and beta-AgI imply lattice mismatches of 4.2 to 7.9%, in a survey of eight common, approximate (non-hybrid) functionals, too large to allow a meaningful contribution from Density Functional Theory to the discussion of the significance of lattice match in ice nucleation.     

On the use of symmetry-adapted crystalline orbitals in SCF-LCAO periodic calculations. I. The construction of the symmetrized orbitals

A computational procedure for generating space-symmetry-adapted Bloch functions (BF) is presented. The case is discussed when BF are built from a basis of local functions (atomic orbitals [AOs]). The method, which is completely general in the sense that it applies to any space group and AOs of any quantum number, is based on the diagonalization of Dirac characters. For its implementation, it does not require as an input character tables or related data, since this information is automatically generated starting from the space group symbol and the AO basis set. Formal aspects of the method, not available in textbooks, are discussed. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 299–309, 1998     

A local density functional—LCAO method with effective potentials for obtaining the electronic structure of molecules and clusters

The introduction of effective core potentials into the Xα LCAO method can greatly expand the size of the molecular system which may be feasibly treated. Therefore, we have incorporated norm-conserving effective potentials into this framework, using a gaussian basis set, for calculations of the electronic structure of molecules and cluster models of solids and surfaces. This combined methodology makes possible the determination of equilibrium geometries and certain aspects of potential surfaces required for a large class of electronic structure problems.     

A comparative study of effective core potential and full-electron calculations in Mo compounds. I. An analysis of topological properties of bond charge distribution

Effective core potential (ECP) and full-electron (FE) calculations for MoS₄^?2, MoO₄^?2, and MoOCl₄ compounds were analyzed. Geometry parameters, binding energies, charge distributions, and topological properties of the electronic density were studied for Mo? L bonds (L = S, O, Cl). Results clearly indicate that those approaches that include valence plus 4s and 4p electrons (ECP2 methods) are able to reproduce the topological properties of Mo? L bonds, charge distributions, and geometries with respect to those obtained by FE methods. ECP methods that consider only the 4d and 5s valence electrons (ECP1) fail in the calculation of molecular properties. The use of 5p functions in ECP1 approaches produces a negative Mulliken charge on Mo. Bader's charges give more consistent results than Mulliken's ones. A new parameter for measuring the degree of ionicity is proposed. © 1994 by John Wiley & Sons, Inc.