Perturbation energy expansions based on two-component relativistic Hamiltonians

The approximate elimination of the small-component approach provides ansätze for the relativistic wave function. The assumed form of the small component of the wave function in combination with the Dirac equation define transformed but exact Dirac equations. The present derivation yields a family of two-component relativistic Hamiltonians which can be used as zeroth-order approximation to the Dirac equation. The operator difference between the Dirac and the two-component relativistic Hamiltonians can be used as a perturbation operator. The first-order perturbation energy corrections have been obtained from a direct perturbation theory scheme based on these two-component relativistic Hamiltonians. At the two-component relativistic level, the errors of the relativistic correction to the energies are proportional to ⁴ Z ⁴, whereas for the relativistic energy corrections including the first-order perturbation theory contributions, the errors are of the order of ⁶ Z ⁶–⁸ Z ⁸ depending on the zeroth-order Hamiltonian.Contribution to the Björn Roos Honorary Issue     

Bond length alternation in ground and HOMO→LUMO excited states in polyenes. Dynamic Stokes shift?

Complete-active-space self-consistent-field calculation of the reorganisation energy, , corresponding to the strongly allowed HOMOLUMO transition in planar polyenes in the trans form (C _{2 h} symmetry), gives >0.5 eV. This large depends on the fact that the short and long bond lengths of the excited ¹B _u (or ³B _u ) state compared to the ¹A _g ground state are almost cancelled. The emission redshift (Stokes shift) in molecules with the same type of system is quite small, however, which suggests that the Stokes shift may be dynamic, owing to the presence of another excited state at lower or about the same energy. Acknowledgement.We congratulate Björn on his birthday and at the same time thank him for the CASSCF method and for many years of collaboration and help from him and his collaborators to make this wonderful method work in our laboratory.Contribution to the Björn Roos Honorary Issue     

Test study on the excitation spectra of the N<Subscript>2</Subscript>–He van der Waals molecule

We have performed ab initio fourth-order Møller–Plesset perturbation theory calculations in the framework of the supermolecule approach on the vertical excitation spectra of the weakly bound van der Waals N₂–He dimer. They indicate a ``T-shaped' stablest ground N<sub>2</sub>(X<sup>1</sup><sub>g</sub><sup>+</sup>)–He(<sup>1</sup>S) electronic state with a well depth, D<sub>e</sub>, of 21.63 cm<sup>–1</sup> at a minimum distance, R<sub>e</sub>, of 3.44 Å and zero-point vibration correction, D<sub>o</sub>, of 7.07 cm<sup>–1</sup>. They also indicate a ``T-shaped' stablest excited conformer with R_e=3.25 Å, D_e=36.85 cm^–1 and D_o=17.06 cm^–1 for the N₂(B³_g)–He(¹S) triplet electronic level. In order to investigate the use of less-demanding correlation methods, test density functional theory calculations using the mPW1PW exchange–correlation functional are also presented for comparison.     

Valence ab initio calculation of the potential-energy curves for the Ca<Subscript>2</Subscript> dimer

The electronic structure of the Ca₂ molecule has been investigated by use of a two-valence-electron semiempirical pseudopotential and applying the internally contracted multireference configuration interaction method with complete-active-space self-consistent-field reference wave functions. Core–valence correlation effects have been accounted for by adding a core-polarization potential to the Hamiltonian. The ground-state properties of the Ca₂ and Ca₂⁺ dimers have also been studied at the single-reference coupled-cluster level with single and double excitations including a perturbative treatment of triple excitations. Good agreement with experiment has been obtained for the ground-state potential curve and the only experimentally known A¹_u⁺ excited state of Ca₂. The spectroscopic parameters D_e and R_e deduced from the calculated potential curves for other states are also reported. In addition, spin–orbit coupling between the singlet and triplet molecular states correlating, respectively, with the (4p)¹P and (4p)³P Ca terms has been investigated using a semi-empirical two-electron spin–orbit pseudopotential. Acknowledgement.This work was supported by grant 5 P03B 082 21 from the Polish State Committee for Scientific Research (KBN).     

A study with a complete-active-space self-consistent-field plus density functional theory combination: The low-lying bound states of N<Subscript>2</Subscript>

The use of a large set of correlation energy functionals, in a post-self-consistent-field procedure, is analyzed for the calculation of the potential-energy curves of the ground state and some excited states in the case of the N₂ molecule. The results show the improvement of the molecular properties, such as dissociation energies, equilibrium bond distances and harmonic vibrational frequencies, (when some of the tested functionals are used), together with the problems that the use of density functional theory functionals applied to multideterminantal wave functions implies. AcknowledgementPartial financial support by the Spanish MCYT, through project BQU2001-0883, is gratefully acknowledged.     

The ground state of TiC revisited

The ground state of TiC is ³⁺, as predicted by previous configuration interaction calculations. It is shown that there are two low-lying ¹⁺ states and that the density functional theory solution corresponds to the higher of the two ¹⁺ states.Contribution to the Björn Roos Honorary Issue     

MP2, DFT‐D,and PCM study of the HMB–TCNE complex: Thermodynamics,electric properties,and solvent effects

Geometry, thermodynamic, and electric properties of the π‐EDA complex between hexamethylbenzene (HMB) and tetracyanoethylene (TCNE) are investigated at the MP2/6‐31G* and, partly, DFT‐D/6‐31G* levels. Solvent effects on the properties are evaluated using the PCM model. Fully optimized HMB–TCNE geometry in gas phase is a stacking complex with an interplanar distance 2.87 × 10^?10 m and the corresponding BSSE corrected interaction energy is ?51.3 kJ mol^?1. As expected, the interplanar distance is much shorter in comparison with HF and DFT results. However the crystal structures of both (HMB)₂–TCNE and HMB–TCNE complexes have interplanar distances somewhat larger (3.18 and 3.28 × 10^?10 m, respectively) than our MP2 gas phase value. Our estimate of the distance in CCl₄ on the basis of PCM solvent effect study is also larger (3.06–3.16 × 10^?10 m). The calculated enthalpy, entropy, Gibbs energy, and equilibrium constant of HMB–TCNE complex formation in gas phase are: ΔH⁰ = ?61.59 kJ mol^?1, ΔS = ?143 J mol^?1 K^?1, ΔG⁰ = ?18.97 kJ mol^?1, and K = 2,100 dm³ mol^?1. Experimental data, however, measured in CCl₄ are significantly lower: ΔH⁰ = ?34 kJ mol^?1, ΔS = ?70.4 J mol^?1 K^?1, ΔG⁰ = ?13.01 kJ mol^?1, and K = 190 dm³ mol^?1. The differences are caused by solvation effects which stabilize more the isolated components than the complex. The total solvent destabilization of Gibbs energy of the complex relatively to that of components is equal to 5.9 kJ mol^?1 which is very close to our PCM value 6.5 kJ mol^?1. MP2/6‐31G* dipole moment and polarizabilities are in reasonable agreement with experiment (3.56 D versus 2.8 D for dipole moment). The difference here is due to solvent effect which enlarges interplanar distance and thus decreases dipole moment value. The MP2/6‐31G* study supplemented by DFT‐D parameterization for enthalpy calculation, and by the PCM approach to include solvent effect seems to be proper tools to elucidate the properties of π‐EDA complexes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Systematic convergence of energies with respect to basis set and treatment of electron correlation: focal-point conformational analysis of methanol

A practical means of overcoming the limitation in accuracy of conformational analysis due to incompleteness of basis sets used in ab initio calculations involves calculating the energy with a series of systematically improving basis sets and extrapolating to the basis set limit. We report here a focal-point conformational analysis for methanol. The Hartree–Fock energy converges exponentially to the basis set limit, while the convergence of second-order correlation energy is well described by the formula . This formula also describes well the convergence of fourth-order correlation energy. The height of the rotational barrier at the Hartree–Fock level can be obtained reliably by taking the difference of the extrapolated energies of the two conformations and correcting the difference for correlation effects. Electron correlation has only a small decreasing effect on the height of the rotational barrier in methanol. The focal-point value for the torsional barrier in methanol is 0.999±0.007 kcal/mol. Acknowledgement.This project was supported by Provost Funds at University of California, Santa Barbara (UCSB). The computational resources were provided partially by the National Computational Science Alliance and UCSBs Supercomputer Facility. We also acknowledge the Horgan Award (University of Missouri-Columbia) to K. K., which made possible the purchase of additional computational resources. We thank Robert Gdanitz and Bernie Kirtman for valuable discussions and Jozef Noga for providing us with a copy of the DIRCCR12-OS program.     

Subshell-pair interelectronic angles of atoms

For the 102 atoms from He to Lr in their ground states, the average interelectronic angles <₁₂> _{nl, n'l'} between an electron in a subshellnl and another electron in a subshell n'l' are examined, where n and l are the principal and azimuthal quantum numbers, respectively. Theoretical study clarifies that <₁₂> _nl,n'l' are 90° precisely if l–l' are even, while they are larger than 90° if l–l' are odd. Numerical analysis of 3,275 subshell pairs with odd l–l' of the 102 atoms shows that the increases in the total average interelectronic angles <₁₂> from 90° are attributed predominantly to subshell pairs with n=n' and l–l'=1.     

Cesium and barium as honorary d elements: CsN7Ba as an example

Quantum chemical calculations suggest that inverse sandwich compounds with the general formula MN₇ M , where M is an alkali metal (K,Rb,Cs), N₇ is a ten--electron ring, and M is an alkaline-earth metal (Ca,Sr,Ba), are local C _7v minima. Among these systems, the CsN₇Ba molecule is the stablest of all and presents a barrier of 35 kcal/mol to dissociation towards CsNBa and three N₂ molecules. Substantial 5d character is found in the bonding. Possible ways of making these high-energy compounds are discussed. AcknowledgementsThis contribution was written in honor of B.O. Roos. The authors thank him for a long and lasting friendship and for inspiring so deeply the scientific career of L. G. This work was partially supported by Ministero dellUniversitáe della Ricerca Scientifica and The Academy of Finland.Contribution to the Björn Honorary Issue     

The electronic spectrum of VCr

The electronic spectrum of VCr has been studied using the complete-active-space self-consistent field complete-active-space second-order perturbation theory approach. Potential-energy curves for 12 electronic states have been computed. Transition energies, with respect to the X² ground state, for some of the calculated electronic states are (with possible experimental values within parentheses) 0.53 eV (0.56) for A²⁺, 1.03 eV (1.14) for A⁴, 1.20 eV (1.14) for B², 1.45 eV (1.51) for B⁴, 1.60 eV (1.51, 1.78) for C², and 1.61 eV (1.63) for A^4–. AcknowledgementsThe research reported in this communication was supported by a grant from the Swedish Natural Science Research Council (NFR). S. Alex and D.G. Leopold are acknowledged for providing results from their negative ion photoelectron spectroscopy on VCr.Contribution to Björn Roos Honorary Issue     

Modeling water exchange on monomeric and dimeric Mn centers

Water exchange on Mn centers in proteins has been modeled with density functional theory using the B3LYP functional. The reaction barrier for dissociative water exchange on [Mn^IV(H₂O)₂(OH)₄] is only 9.6 kcal mol^–1, corresponding to a rate of 6×10⁵ s^–1. It has also been investigated how modifications of the model complex change the exchange rate. Three cases of water exchange on Mn dimers have been modeled. The reaction barrier for dissociative exchange of a terminal water ligand on [(H₂O)₂(OH)₂Mn^IV(-O)₂Mn^IV(H₂O)₂(OH)₂] is 8.6 kcal mol^–1, while the bridging oxo group exchange with a ring-opening mechanism has a barrier of 19.2 kcal mol^–1. These results are intended for interpretations of measurements of water exchange for the oxygen evolving complex of photosystem II. Finally, a tautomerization mechanism for exchange of a terminal oxyl radical has been modeled for the synthetic O₂ catalyst [(terpy)(H₂O)Mn^IV(-O)₂Mn^IV(O)(terpy)]³⁺ (terpy=2,2:6,2-terpyridine). The calculated reaction barrier is 14.7 kcal mol^–1.Contribution to the Björn Roos Honorary Issue     

Simple molecular wavefunctions with correlation corrections II

The potential curves for the ground state of Li₂ (¹ _g ⁺ ) and FH (¹ _g ⁺ ) are computed. The correlation energy is calculated using a functional of the one- and two-electron density matrices derived from an MC SCF reference wavefunction and is added to the reference energy to obtain a correlated potential curve.     

The migratory insertion of carbon monoxide and methyl isocyanide into zirconium–carbon and titanium–carbon bonds anchored to a calix[4]arene moiety: a dynamical density functional study

The energetics and reaction mechanism of the migratory insertion of carbon monoxide and methyl isocyanide into the zirconium–carbon and titanium–carbon bonds in [calix[4](OMe)₂(O)₂–M–Me₂], (M=Zr, Ti), have been investigated by combining static and dynamic density functional calculations. Two steps have been characterized: the coordination of the incoming nucleophilic moiety leading to relatively stable facial adducts; its subsequent insertion into the M–C bond, leading to ²-bound acyl or iminoacyl complexes, providing a rationale for the different behavior of CO and MeNC towards both insertion and deinsertion reactions. Our results indicate that the rate-determining step for the overall MeNC insertion into the M–C bond is its coordination to the electron-deficient metal center, with the titanium system featuring a higher energy barrier (12.7 versus 5.5 kcal mol^–1). Ab initio molecular dynamics simulations have been performed on the Zr system by means of the Car–Parrinello method, to study the hitherto inaccessible mechanistic features of the insertion reactions.Contribution to the Björn Roos Honorary Issue     

MD Simulation of an Infinitely Dilute Aqueous Solution of Formamide. Study of Thermodynamic, Structural, Dynamic, and Spectroscopic Properties

A molecular dynamics simulation of an infinitely dilute aqueous solution of formamide was carried out using an MP2-CP ab initio potential to describe the solute–solvent interaction. Various static and dynamic properties were calculated using this potential obtained by fitting the formamide–water interaction energies to a 12-6-1 type function. These energies were calculated with the supermolecular approach by considering the MP2 correlation and the CP superposition. The values presented for the thermodynamic functions (H _S–W = –25.5 kcal-mol^–1 and G _S–W = –15.9 kcal-mol^–1), the structure of the first hydration layer (with 5 to 6 solvent molecules bonded to the solute), the solute's translational (D= 1.50 × 10^–5 cm²-s^–1) and rotational ( = 6.6 ps) mobility in the surrounding medium, and the positions of the H···O hydrogen bond spectral bands corresponding to these motions (_i = 92, 246, 379, and 636 cm^–1), are in agreement with the available results for this and other similar systems. In addition, the results are compared with those obtained by using parameters transferred from other systems. We observed that these values depend strongly on the potential used and concluded that it is advisable to avoid the use of such parameters.     

Electric properties of the chloride ion

The dipole (), quadrupole (C), and dipole-quadrupole (B) polarizabilities and the dipole hyperpolarizability () of the chloride ion have been calculated by using the many-body perturbation theory approach and a series of large polarized GTO/CGTO basis sets. The complete fourth-order treatment of the electron correlation effects with a basis set comprising the s, p, d, f, and g functions gives: =38.01 a.u., C=211.5 a.u., B=–5.14×10³ a.u., and =128. 5×10³ a.u. as compared to the corresponding SCF values (=31.49 a.u., C=158.9 a.u., B=–2.92×10³ a.u., =57.7×10³ a.u.). The quenching of polarizabilities of the Cl^– ion in solutions and ionic crystals is discussed.     

Magnetization of ferromagnetic clusters

The magnetization and deflection profiles of magnetic clusters in a Stern-Gerlach magnet are calculated for conditions under which the magnetic moment is fixed in the intrinsic frame of the cluster, and the clusters enter the magnetic field adiabatically. The predicted magnetization is monotonic as a function of the ratio of magnetic energy ₀ B to the rotational thermal energyk _BT. In low field the average magnetization is 2/3 of the Langevin function. The high-field moment approaches saturation asymptotically asB ^–1/2 instead of theB ^–1 dependence in the Langevin function     

He 2++ molecular ion in a strong time-dependent magnetic field: a current-density functional study

The He molecular ion exposed to a strong ultrashort time‐dependent (TD) magnetic field of the order of 10⁹ G is investigated through a quantum fluid dynamics (QFD) and current‐density functional theory (CDFT) based approach using vector exchange‐correlation (XC) potential and energy density functional that depend not only on the electronic charge‐density but also on the current density. The TD‐QFD‐CDFT computations are performed in a parallel internuclear‐axis and magnetic field‐axis configuration at the field‐free equilibrium internuclear separation R = 1.3 au with the field‐strength varying between 0 and 10¹¹ G. The TD behavior of the exchange‐ and correlation energy of the He is analyzed and compared with that obtained using a [B‐TD‐QFD‐density functional theory (DFT)] approach based on the conventional TD‐DFT under similar computational constraints but using only scalar XC potential and energy density functional dependent on the electronic charge‐density alone. The CDFT based approach yields TD exchange‐ and correlation energy and TD electronic charge‐density significantly different from that obtained using the conventional TD‐DFT based approach, particularly, at typical magnetic field strengths and during a typical time period of the TD field. This peculiar behavior of the CDFT‐based approach is traced to the TD current‐density dependent vector XC potential, which can induce nonadiabatic effects causing retardation of the oscillating electronic charge density. Such dissipative electron dynamics of the He molecular ion is elucidated by treating electronic charge density as an electron‐“fluid” in the terminology of QFD. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Dynamics and structural changes of small water clusters on ionization

Despite utmost importance in understanding water ionization process, reliable theoretical results of structural changes and molecular dynamics (MD) of water clusters on ionization have hardly been reported yet. Here, we investigate the water cations [(H₂O)_{n = 2–6}⁺] with density functional theory (DFT), Möller–Plesset second‐order perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. The complete basis set limits of interaction energies at the CCSD(T) level are reported, and the geometrical structures, electronic properties, and infrared spectra are investigated. The characteristics of structures and spectra of the water cluster cations reflect the formation of the hydronium cation moiety (H₃O⁺) and the hydroxyl radical. Although most density functionals fail to predict reasonable energetics of the water cations, some functionals are found to be reliable, in reasonable agreement with high‐level ab initio results. To understand the ionization process of water clusters, DFT‐ and MP2‐based Born‐Oppenheimer MD (BOMD) simulations are performed on ionization. On ionization, the water clusters tend to have an Eigen‐like form with the hydronium cation instead of a Zundel‐like form, based on reliable BOMD simulations. For the vertically ionized water hexamer, the relatively stable (H₂O)₅⁺ (5sL4A) cluster tends to form with a detached water molecule (H₂O). © 2013 Wiley Periodicals, Inc.