Hartree-Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms.

An implementation of the Hartree-Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be ZHFC=1.031 177 528.This article is part of the theme issue 'Modern theoretical chemistry'.

Combining Sanford Arylations on Benzodiazepines with the Nuisance Effect.

5-Phenyl-1,3-dihydro-2H-1,4-benzodiazepin-2-ones react under palladium- and visible light photoredox catalysis, in refluxing methanol, with aryldiazonium salts to afford the respective 5-(2-arylphenyl) analogues. With 2- or 4-fluorobenzenediazonium derivatives, both fluoroaryl- and methoxyaryl- products were obtained, the latter resulting from a SNAr on the fluorobenzenediazonium salt ("nuisance effect"). A computational DFT analysis of the palladium-catalysed and the palladium/ruthenium-photocalysed mechanism for the functionalization of benzodiazepines indicated that, in the presence of the photocatalyst, the reaction proceeds via a low-energy SET pathway avoiding the high-energy oxidative addition step in the palladium-only catalysed reaction pathway.

Gas phase UV spectrum of a Cu(II)-bis(benzene) sandwich complex: experiment and theory.

Photofragmentation with tunable UV radiation has been used to generate a spectrum for the copper-bis(benzene) complex, [Cu(C6H6)2](2+), in the gas phase. The ions were held in an ion trap where their temperature was reduced to ∼150 K, whereby the spectrum revealed two broad features at ∼38,200 and ∼45,700 cm(-1). Detailed calculations using density functional theory (DFT) show the complex can occupy three minimum energy structures with C2v and C2 (staggered and eclipsed) symmetries. Adiabatic time-dependent DFT (TDDFT) has been used to identify electronic transitions in [Cu(benzene)2](2+), and the calculations show these to fall into two groups that are in excellent agreement with the experimental data. However, the open-shell electronic configuration of Cu(2+) (d(9)) may give rise to excited states with double-excitation character, and the single-excitation adiabatic TDDFT treatment leads to extensive spin contamination. By quantifying the extent of spin contamination and allowing for the inclusion of a small percentage (∼10%), the theory can provide quantitative agreement with the experimental data.

Predicting the stability of atom-like and molecule-like unit-charge Coulomb three-particle systems.

Non-relativistic quantum chemical calculations of the particle mass, m±2, corresponding to the dissociation threshold in a range of Coulomb three-particle systems of the form m±1m±2m±3, are performed variationally using a series solution method with a Laguerre-based wavefunction. These masses are used to calculate an accurate stability boundary, i.e., the line that separates the stability domain from the instability domains, in a reciprocal mass fraction ternary diagram. This result is compared to a lower bound to the stability domain derived from symmetric systems and reveals the importance of the asymmetric (mass-symmetry breaking) terms in the Hamiltonian at dissociation. A functional fit to the stability boundary data provides a simple analytical expression for calculating the minimum mass of a third particle required for stable binding to a two-particle system, i.e., for predicting the bound state stability of any unit-charge three-particle system.

Computational study of the coordination of methane to first row transition metal dication complexes.

The coordination of methane, the first step in methane activation, to coordinately unsaturated first row transition metal dication complexes has been studied computationally to determine the most stable metal-methane interaction. The geometries and the vibrational frequencies of the encounter complexes [M(pyridine)2(CH4)](2+) have been determined using density functional theory with the ωB97XD hybrid functional and triple-ζ basis sets. The structure is dependent on the metal center; for the early transition metals η(3) coordination is favored, whereas η(2) is more favorable for the later transition metals. The periodic trend in methane binding energies in the [M(pyridine)2(CH4)](2+) complexes follows the trend in electron affinity until the Mn complex but then exhibits decreasing energies from Fe to Zn. This is attributed to increasing Pauli repulsion and ligand-ligand repulsion. For the most stable complex, [Cr(pyridine)2(CH4)](2+), the structures, energies, and spin states of the key intermediates and products in the oxidative addition/reductive elimination pathway have been investigated. It is found that the reaction is thermodynamically favorable and indicates that two-state reactivity may play an important role in lowering the energy of the hydridomethyl intermediate.

The stability of S-states of unit-charge Coulomb three-body systems: from H- to H2(+).

High accuracy non-relativistic quantum chemical calculations of the ground state energies and wavefunctions of symmetric three-particle Coulomb systems of the form {m1(±)m2(±)m3(∓)}, m1 = m2, are calculated using an efficient and effective series solution method in a triple orthogonal Laguerre basis set. These energies are used to determine an accurate lower bound to the stability zone of unit-charge three-particle Coulomb systems using an expression for the width of the stability band in terms of g, the fractional additional binding due to a third particle. The results are presented in the form of a reciprocal mass fraction ternary diagram and the energies used to derive a parameterised function g(a3), where a3=m3 (-1)/(m1(-1)+m2(-1)+m3(-1)) is the reciprocal mass of the uniquely charged particle. It is found that the function is not minimal at a3 = 0 which corresponds to ∞H(-) nor is it minimal at the positronium negative ion (Ps(-)) the system with the least absolute energetic gain by association with a third particle; the function g(a3) is minimal at m1∕m3 = 0.49, and a possible physical interpretation in terms of the transition from atomic-like to molecular-like is provided.

Conformation-resolved UV spectra of Pb(II) complexes: a gas phase study of the sandwich structures [Pb(toluene)2]2+ and [Pb(benzene)2]2+.

Toxic heavy metals, such as Pb(2+), have become important targets for the development of efficient receptors that are capable of recognizing their presence as environmental and biological pollutants, and an important part of that receptor-metal characterization process is the provision of spectral evidence that identifies the presence of a metal ion. From results reported here on a combined experimental and theoretical study it is shown that, when complexed with aromatic ligands, Pb(2+) is capable of yielding structured UV spectra, which: (i) exhibit discrete electronic transitions that include significant contributions from the metal ion; (ii) are very sensitive to the electronic properties of coordinating ligands; and (iii) are sensitive to subtle changes in coordination geometry. Two aromatic sandwich complexes, [Pb(benzene)2](2+) and [Pb(toluene)2](2+) have been prepared in the gas phase and their UV action spectra recorded from ions held and cooled in an ion trap. Whilst [Pb(benzene)2](2+) exhibits a spectrum with very little detail, that recorded for [Pb(toluene)2](2+) reveals a rich structure in the wavelength range 220-280 nm. Theory in the form of density functional theory (DFT) shows that both types of complex take the form of hemidirected structures, and that [Pb(toluene)2](2+) can adopt three distinct conformers depending upon the relative positions of the two methyl groups. Further calculations, using adiabatic time-dependent DFT to assign electronic transitions, provide evidence of individual [Pb(toluene)2](2+) conformers having been resolved in the experimental spectrum. Of particular significance for the development of methods for identifying Pb(2+) as an environmental or biological pollutant, is the observation that there are distinct ligand-to-metal charge transfer transitions in the UV that are sensitive to both the geometry and the electronic characteristics of molecules that accommodate the metal ion.

Correlated energy from radial density-energy relations.

Here, we demonstrate that the radial distribution function can be mapped into a radial density-energy space and the relationship between the radial density and radial energy is linear for the ground and excited states of helium-like systems; the gradient of the resulting straight line delivers the energy of the state considered. To utilize this finding, a simple analytical expression for the total energy in terms of the density at the most probable nucleus-electron distance of the systems considered is derived using a fitting procedure.

Moderating the acidity of Pb(II)-water complexes through the coordination of nonaqueous ligands: a computational study.

The metal dication Pb(II) is known to promote catalytic cleavage of the sugar-phosphate backbone in tRNA. The mechanism proposed to achieve this step requires that the [Pb(II)OH(-)](+) moiety act as a nucleophile and alter the local acidity of surrounding water molecules. MP2 calculations investigating the effect that nonaqueous bases have on the stability of dihydrated-Pb(II) show that the height and position of the proton-transfer barrier are sensitive to the presence of a single N- or O-coordinating "spectator" ligand and that, with the addition of two ligands coordinated directly to the Pb(II) center, the equilibrium for the hydrolysis reaction can shift to the left, thus making the Pb(II)-hydrate complex more stable than the Pb(II)-hydroxide complex. The calculations reveal a good correlation between the gas-phase basicities of nonaqueous ligands coordinated to the metal center and the barriers to proton transfer in [Pb(H(2)O)(2)](2+). In terms of the Pb(II)-induced hydrolysis of tRNA, these results indicate that the coordination of [Pb(II)-OH(-)](+) to uracil and cytosine in tRNA increases the basicity of the hydroxyl group and promotes nucleophilic attack of H(+).

Reparametrization of the Colle-Salvetti formula.

We investigate the Colle-Salvetti (CS) formula, the basis of the Lee, Yang and Parr (LYP) correlation functional used in approximate density functional theory. The CS formula is reparametrized using high-accuracy Hartree-Fock (HF) wavefunctions to determine the accuracy of the formula to calculate anions. Fitting to the hydride ion or the two-electron system just prior to electron detachment at the HF level of theory does not, in general, improve the calculated correlation energies using the parameters derived from the CS/LYP method. An analysis of the CS parameters used in the popular LYP functional demonstrates the ingenuity and perhaps fortuitousness of the original formulation by CS.

Activation of carbon dioxide by divalent tin alkoxides complexes.

A series of terminal tin(II) alkoxides have been synthesized utilizing the bulky ß-diketiminate ligand [{N(2,6-(i)Pr(2)C(6)H(3))-C(Me)}(2)CH] (BDI). The nucleophilicities of these alkoxides have been examined, and unexpected trends were observed. For instance, (BDI)SnOR only reacts with highly activated aliphatic electrophiles such as methyl triflate, but reacts reversibly with carbon dioxide. Both the rate of reaction and the degree of reversibility is dependent upon minor changes in the alkoxide ligand, with the bulkier tert-butoxide ligand displaying slower reactivity than the corresponding isopropyl ligand, although the latter system is a more exergonic reaction. Density Function Theory (DFT) calculations show that the differences in the reversibility of carbon dioxide insertion can be attributed to the ground-state energy differences of tin alkoxides while the rate of reaction is attributed to relative bond strengths of the Sn-O bonds. The mechanism of carbon dioxide insertion is discussed.

Ultraviolet photofragmentation spectroscopy of alkaline earth dication complexes with pyridine and 4-picoline (4-methyl pyridine).

A detailed experimental and theoretical study has been undertaken of the UV photofragmentation spectroscopy of the alkaline earth metal dications Mg(2+), Ca(2+), and Sr(2+) complexed with pyridine and 4-methyl pyridine (4-picoline). The ion complexes have been prepared using the pick-up technique and held in an ion trap where their internal temperature has been reduced to <150 K. Exposure of the trapped ions to tunable UV laser radiation leads to the appearance of photofragments with intensities that show significant variation as a function of wavelength. For all three metal dications, the resultant spectra show evidence of resolved features. Time-dependent density functional theory (TDDFT) has been used to identify possible electronic transitions that might be present in the [M(pyridine)(4)](2+) complexes (M = Mg, Ca, and Sr) within the wavelength range studied. These calculations show that the spectra are dominated by strong π* ← π and weaker π* ← n transitions localized on the pyridine ligands. The calculations correctly identify those regions of the experimental spectra where UV transitions begin to occur in the complexes and also the wavelengths at which absorption maxima are reached; however, more subtle features of the spectra are difficult to assign with confidence.

Electron correlation in Li+, He, H- and the critical nuclear charge system Z C : energies, densities and Coulomb holes.

This paper presents high-accuracy correlation energies, intracule densities and Coulomb hole(s) for the lithium cation, helium, hydride ion and the system with the critical nuclear charge, Z C , for binding two electrons. The fully correlated (FC) wave function and the Hartree-Fock (HF) wave function are both determined using a Laguerre-based wave function. It is found that for the lithium cation and the helium atom a secondary Coulomb hole is present, in agreement with a previous literature finding, confirming a counterintuitive conclusion that electron correlation can act to bring distant electrons closer together. However, no evidence for a tertiary Coulomb hole is found. For the hydride anion and the system just prior to electron detachment only a single Coulomb hole is present and electron correlation decreases the probability of finding the electrons closer together at all radial distances. The emergence of a secondary Coulomb hole is investigated and found to occur between Z = 1.15 and Z = 1.20. The FC and HF energies and intracule densities (in atomic units) used to calculate the correlation energy and Coulomb hole, respectively, are accurate to at least the nano-scale for helium and the cation and at least the micro-scale for the anions.

A gas-phase study of the preferential solvation of Mn(2+) in mixed water/methanol clusters.

The kinetic shift that exists between two competing unimolecular fragmentation processes has been used to establish whether or not gas-phase Mn(2+) exhibits preferential solvation when forming mixed clusters with water and methanol. Supported by molecular orbital calculations, these first results for a metal dication demonstrate that Mn(2+) prefers to be solvated by methanol in the primary solvation shell.

State-resolved UV photofragmentation spectrum of the metal dication complex [Zn(pyridine)(4)](2+).

A combined theoretical and experimental study of electronic transitions in the complex [Zn(pyridine)(4)](2+) provides the first example of a state-resolved electronic spectrum to be recorded for a dication complex in the gas phase.

A synthetic, catalytic and theoretical investigation of an unsymmetrical SCN pincer palladacycle.

The SCN ligand 2-{3-[(methylsulfanyl)methyl]phenyl}pyridine, 1, has been synthesized starting from an initial Suzuki-Miyaura (SM) coupling between 3-((hydroxymethyl)phenyl)boronic acid and 2-bromopyridine. The C-H activation of 1 with in situ formed Pd(MeCN)4(BF4)2 has been studied and leads to a mixture of palladacycles, which were characterized by X-ray crystallography. The monomeric palladacycle LPdCl 6, where L-H = 1, has been synthesized, and tested in SM couplings of aryl bromides, where it showed moderate activity. Density functional theory and the atoms in molecules (AIM) method have been used to investigate the formation and bonding of 6, revealing a difference in the nature of the Pd-S and Pd-N bonds. It was found that S-coordination to the metal in the rate determining C-H bond activation step leads to better stabilization of the Pd(II) centre (by 13-28 kJ mol(-1)) than with N-coordination. This is attributed to the electron donating ability of the donor atoms determined by Bader charges. The AIM analysis also revealed that the Pd-N bonds are stronger than the Pd-S bonds influencing the stability of key intermediates in the palladacycle formation reaction pathway.

The nature of the bonding in symmetrical pincer palladacycles.

The accuracy of DFT-optimised geometries of the symmetrical pincer palladacycles PdNCN and PdSCS, [ClPd{2,6-(Me2NCH2)2C6H3}] and [ClPd{2,6-(MeSCH2)2C6H3}] respectively, has been evaluated by investigating the performance of eight commonly used density functionals with four combinations of basis set, in reproducing their X-ray crystal structures. It was found that whilst the ωB97XD functional performed best over all, the PBE and TPSS functionals performed best when considering the palladium coordination geometry. The role of the donor atom in the stability and reactivity of the symmetric palladacycles, PdYCY, Y = N, S, or P, has been determined using Bader's Atoms in Molecules method to elucidate the nature of the bonding, and using a model formation reaction, which involves the C-H activation of the pincer ligand YCY by PdCl2. The calculations reveal distinct differences in the bond strength and nature of the interaction of Pd with the donor atoms Y, which support differences in the thermodynamic stability of the palladacycles.

Evidence of zinc superoxide formation in the gas phase: comparisons in behaviour between ligated Zn(I/II) and Cu(I/II) with regard to the attachment of O2 or H2O.

Singly and doubly charged atomic ions of zinc and copper have been complexed with pyridine and held in an ion trap. Complexes involving Zn(II) and Cu(I) (3d(10)) display a strong tendency to bind with H(2)O, whilst the Zn(I) (3d(10)4s(1)) complexes exhibit a strong preference for the attachment of O(2). DFT calculations show that this latter result can be interpreted as internal oxidation leading to the formation of superoxide complexes, [Zn(II)O(2)(-)](pyridine)(n), in the gas phase. The calculations also show that the oxidation of Zn(I) to form Zn(II)O(2)(-) is promoted by a mixing of the occupied 4s and vacant 4p orbitals on the metal cation, and that this process is facilitated by the presence of the pyridine ligands.

Ligand field photofragmentation spectroscopy of [Ag(L)N]2+ complexes in the gas phase: experiment and theory.

Experiments have been undertaken to record photofragmentation spectra from a series of [Ag(L)N]2+ complexes in the gas phase. Spectra have been obtained for silver(II) complexed with the ligands (L): acetone, 2-pentanone, methyl-vinyl ketone, pyridine, and 4-methyl pyridine (4-picoline) with N in the range of 4-7. A second series of experiments using 1,1,1,3-fluoroacetone, acetonitrile, and CO2 as ligands failed to show any evidence of photofragmentation. Interpretation of the experimental data has come from time-dependent density functional theory (TDDFT), which very successfully accounts for trends in the spectra in terms of subtle differences in the properties of the ligands. Taking a sample of three ligands, acetone, pyridine, and acetonitrile, the calculations show all the spectral transitions to involve ligand-to-metal charge transfer, and that wavelength differences (or lack of spectra) arise from small changes in the energies of the molecular orbitals concerned. The calculations account for an absence in the spectra of any effects due to Jahn-Teller distortion, and they also reveal structural differences between complexes where the coordinating atom is either oxygen or nitrogen that have implications for the stability of silver(II) compounds. Where possible, comparisons have also been made with the physical properties of condensed phase silver(II) complexes.