A theoretical investigation of the oxidation states of palladium complexes and their role in the carbonylation reaction

Two different, yet related, topics are discussed: (i) the reduction of palladium (II) in Pd(OAc)₂ complexes reacting with phenyl phosphines and leading to Pd(0) phosphine complexes, and (ii) the carbonylation reaction of allyl chlorides catalyzed by these Pd(0) species. The results show that the overall reduction is an exothermic process that can be accomplished along two different reaction paths, one being clearly favoured over the other. Similarly, three different channels have been determined for the carbonylation reaction that primarily differ in the timing and the way in which the reacting species bind the metal. In the first path (the σ-path), the allyl fragment interacts very weakly with the metal, whereas the CO molecule strongly binds it and reacts with the allyl. The second channel (the π–η³ pathway) is characterized by a π–η³ interaction between the allyl fragment and the palladium, to which the CO molecule binds, before the two units react affording the product. In both cases, two consecutive migrations of the chlorine ‘assist’ the course of the reaction. In the third case (the η² pathway) the allyl fragment initially enters the palladium coordination sphere, and the CO molecule then simultaneously binds it and the phosphorous atom of one phosphine ligand. The first two paths are favoured.     

Theoretical studies on the anisotropy of the first hyperpolarizabilities of one- and two-dimensional charge-transfer molecules: role of solvent polarity

The effects of solvent polarity on the geometry and static first hyperpolarizability of one- and two-dimensional charge transfer molecules based on para-nitroaniline (PNA) and 1,3-diamino-4,6-dinitrobenzene (DADB) were studied using a polarizable continuum model (PCM) at the B3LYP/6-31+G(d,p) level of theory. The inclusion of solvent does not change the geometry significantly, but produces a change in the calculated results of the electronic structures and nonlinear optical properties. It is found that solvent polarity has an important influence on the first hyperpolarizability, whereas its influence is negligible on the nonlinearity anisotropy parameter both for PNA and DADB, due to the fact that the off-diagonal component and the diagonal component of the first hyperpolarizability possess similar solvent effect characteristics.     

Analysis of multi-configuration density functional theory methods: theory and model application to bond-breaking

We consider the extension of the standard single-determinant Kohn–Sham method to the case of a multi-configuration auxiliary wave function. By applying the rigorous Kohn–Sham method to this case, we construct the proper interacting and auxiliary energy functionals. Following the Hohenberg–Kohn theorem for both energy functionals, we derive the corresponding multi-configuration Kohn–Sham equations, based on a local effective potential. At the end of the analysis we show that, at the ground state, the auxiliary wavefunction must collapse into a single-determinant wave function, equal to the regular KS wavefunction. We also discuss the stability of the wavefunction in multi-configuration density functional theory methods where the auxiliary system is partially interacting, and the remaining (residual) correlation is evaluated as a functional of the density. As an example showing both the challenges and the possibilities, we implement such a procedure for the perfect pairing wavefunction, using a residual correlation functional that is based on the Lee–Yang–Parr functional, and present results for an elementary bond-breaking process.     

Nonlinear optical and structural properties of M@C N endohedrals (M = Li,Ca and Sc,N = 60 and 70)

We have investigated the static (ω = 0) and frequency-dependent nonlinear optical (NLO) properties of the M@C _N endohedrals (M = Li, Ca, Sc, N = 60 and 70) using the SSH (Su–Schrieffer–Heeger) approximation and sum-over-state (SOS) approach. Also, we study the effects of displacement and alkali, alkaline earth and lanthanide metal atoms and type of cage on the hyperpolarisabilities of the M@C _N endohedrals. The hyperpolarisability magnitudes and spectra are in agreement with experiment and the work of others using the SSH approximation. Our results indicate that the cage-type effect on the NLO spectra of M@C _N endohedrals is dramatic. Also, atom type has little effect on the highest peak value. These relationships between the atom and cage type and hyperpolarisability values may be beneficial to experimentalists when designing new NLO materials with large NLO responses.     

Effect of curve crossing on absorption and resonance Raman spectra: analytical treatment for delta-function coupling in parabolic potentials

We propose an exactly solvable model for the two-state curve-crossing problem. Our model assumes the coupling to be a delta function. It is used to calculate the effect of curve crossing on the electronic absorption spectrum and the resonance Raman excitation profile.     

Direct ab initio dynamics calculations of the reaction rate for the hydrogen abstraction reaction of NCO with CH4 and C2H6

The kinetics of the hydrogen abstraction reactions NCO + CH₄ (R1) and NCO + C₂H₆ (R2) have been studied over a wide temperature range. The minimum energy paths (MEPs) were calculated at the MP2/cc-pVDZ level and single-point calculations were refined at the G3MP2 level. The rate constants for the title reactions were calculated using canonical variational transition state theory (CVT) with small-curvature tunneling (SCT) contributions. The fitted three-parameter formulae are k ₁ = 2.52 × 10^?22 T ^3.46 exp(2466/T) and k ₂ = 9.8 × 10^?22 T ^3.2 exp(411.8/T) cm³ molecule^?1 s^?1 for (R1) and (R2), respectively. The calculated rate constants were found to be in good agreement with the available experimental data. Deuterium kinetic isotope effects were also investigated. Both reactions show a significant kinetic isotope effect in the low-temperature range.     

Penalty functions for combining coupled-cluster and perturbation amplitudes in local correlation methods with optimized orbitals

Local active space correlation models based on the coupled-cluster doubles (CCD) model like Generalized Valence Bond Perfect Pairing (GVB-PP) and Imperfect Pairing (IP) are attractive methods for treating electron correlation, because they are computationally inexpensive and can describe strong correlations. However, they suffer from symmetry-breaking (SB) in systems with multiple resonance structures, which arises due to neglected correlations. We investigate the extent to which these problems can be removed by using second-order perturbation theory (PT) for weak correlations coupling three different electron pairs, and (infinite-order) coupled-cluster (CC) theory for stronger correlations involving electrons in only one or two pairs. The resulting Three-Pair Corrected Imperfect Pairing (TIP) method is explored here, and it is shown that to robustly combine CC and PT it is necessary to modify several aspects of the basic method. Most importantly, a penalty function term is introduced to ensure the PT amplitudes remain small. Comparison against CC treatment of the three-pair correlations suggests penalty terms will be beneficial for any hybrid CC/PT method that includes orbital optimization. The TIP method greatly reduces SB in aromatic hydrocarbons and recovers a significantly higher fraction of the valence electron correlation energy than IP.     

The accuracy of local MP2 methods for conformational energies

The relative energies of 95 conformers of four peptide models are studied using MP2 and LMP2 methods and correlation consistent basis sets ranging from double-zeta to augmented quintuple-zeta quality. It is found that both methods yield quite similar results, and the differences between MP2 and LMP2 decrease systematically with increasing basis set. Due to reduced intramolecular basis set superposition effects (BSSE), the LMP2 results converge more slowly to the basis set limit for most of these rather small systems. However, for larger peptides, the BSSE has a very large effect on the energy difference between extended and helical structures, leading to a very strong basis set dependence of the canonical MP2 results. It is demonstrated for alanine octapeptides that the basis set error exceeds 30 and 20kJ mol^?1, respectively, if augmented double-zeta and triple-zeta basis sets are used. On the other hand, the LMP2 results are only slightly affected by the basis set size, and, even with augmented double-zeta basis sets, reasonably accurate results are obtained. Furthermore, for the larger systems, the computation times for the LMP2 calculations are shown to be up to one order or magnitude shorter than for canonical MP2 calculations with the same basis set.     

Theoretical study and rate constant calculation for the O(3P) + C2H5CN reaction

The complicated microscopic reaction mechanisms of O(³P) with C₂H₅CN on the ground electronic state energy surface have been investigated at the G3(MP2) level of theory based on the geometric parameters optimized at the B3LYP/6-311 + G(d, p) level. Two kinds of H-abstraction and addition–elimination channels are considered, namely methylene-H abstraction, methyl-H abstraction, C-addition/elimination and N-addition/elimination. The kinetics of the title reaction have been studied using the TST and multichannel RRKM methodologies over a wide temperature range of 200–2000 K. The results show that the methylene-H abstraction process is predominant for the whole reaction. With an increase of temperature, H-abstraction from the methyl position channel should be taken into account. The C-addition/elimination process provides a few contributions to the title reaction compared with two kinds of H-abstraction channels over the whole temperature region and the N-addition/elimination channel can be negligible due to the high entrance barrier and unstable products.     

A generalized Langevin algorithm for studying permeation across biological ion channels

We present a new leapfrog algorithm for the numerical solution of the generalized Langevin equation (GLE) in the case where the friction kernel is exponentially decaying. Like other leapfrog and Verlet algorithms, our algorithm is second order in velocity and third order in position. It is relatively easy to implement compared with other available algorithms, and would therefore make a good candidate for exploring the effects of finite memory time-scales in situations where modelling the precise functional form of the memory kernel was not important. We have tested this algorithm on a one-dimensional barrier crossing model, and found good asymptotic agreement with limits obtained using Brownian dynamics (BD) simulations, as well as with a theoretical asymptotic limit. We have also used the algorithm to perform a more sophisticated simulation of ion conduction through a KcsA channel. The results are a close match to corresponding results obtained using the Langevin equation, thereby helping to justify the use of Brownian dynamics in KcsA and other similar ion channels.     

Quantum chemical study of the ground-state alcoholic complexation of selected dual luminescent compounds

The ground- and excited-state features of dual luminescent molecules are strongly influenced by the presence of alcoholic additives. Selected ground-state properties of methanol and 1,1,1,3,3,3-hexafluoro-propan-2-ol complexes of 4-aminobenzonitrile, 4-aminopyridine and aniline derivatives were obtained by quantum chemical calculations. The formation enthalpies of the complexes are the most exothermic when the cyano or ring nitrogen interacts with the hydroxyl group of the alcohols. The binding energies are almost doubled when the fluorinated reactant is the hydrogen bond donor. Parallel to the enhancement of the stabilization of the complex, the ground-state dipole moment also increases notably with complex formation. In principle, consideration of this increase is essential in interpretation of the solvatochromatic behaviour of the complexed species.     

Proximity vs. strain in intramolecular ring-closing reactions

The DFT and ab initio calculation results for ring-closing reactions of eight different ω-bromoalkanecarboxylate anions (1–8) reveal that the activation energy (ΔG ^?) for the intramolecular cyclization process is strongly correlated with both (i) the experimental intramolecular cyclization rate (log k _intra) and (ii) the distance between the two reactive centres, whereas the slope values of the change in enthalpy (ΔH) vs. the attack angle (α) and the distance between the two reacting centres (r) were found to correlate strongly with the experimental strain energy of the cycle being formed (E _{s Exp}). These results assist in designing pro-prodrug systems that can be utilized to improve the overall biopharmaceutical profile of current medications in order to enhance their effectiveness and ease their utility.     

A unified description of sum frequency generation,parametric down conversion and two-photon fluorescence

A superoperator non-equilibrium Green's function formalism is presented for computing nonlinear optical processes involving any combination of classical and quantum optical modes. Closed correlation-function expressions based on superoperator time-ordering are derived for the combined effects of causal response and non-causal spontaneous fluctuations. Coherent three wave mixing (sum frequency generation and parametric down conversion) involving one and two quantum optical modes, respectively, are compared with their incoherent counterparts: two-photon-induced fluorescence and two-photon-emitted fluorescence.     

Concentration and temperature dependent interaction studies using dielectric and thermodynamic methods on mixtures of anisole with o-toluidine and m-toluidine

Molecular interactions in mixtures of anisole with o-toluidine and anisole and m-toluidine have been studied at three different temperatures using the dielectric method with measurements of the static permittivity and permittivity at optical frequency. From the measured values, the Kirkwood correlation parameter, Bruggeman parameter, excess permittivity and thermodynamic excess free energy were computed for the mixtures. Positive and negative values of excess permittivity were obtained for both mixtures. The excess free energy for the anisole+o-toluidine mixture is positive at all three temperatures, whereas mixed values (positive and negative) are obtained for the anisole+m-toluidine mixture. Alignment of the dipoles in both mixtures was identified by Kirkwood factors. The investigation shows that the interaction between the components changes systematically with concentration and temperature and the change is minimum.     

Electronic structure,absorption spectra,and hyperpolarisabilities of some novel push–pull zinc porphyrins. A DFT/TDDFT study

DFT/TDDFT calculations have been performed on some novel push–pull zinc porphyrins (denoted ZnPor 1, ZnPor 2, and ZnPor 3). This theoretical work aims to investigate the electronic structure, absorption spectra, and hyperpolarisabilities of these molecules. To examine the effects of the peripheral substituents on the molecular properties, zinc porphine (ZnP) and zinc tetraphenylporphine (ZnTPP) were also included in the study. The orbital energy level patterns of the substituted zinc porphyrins are indeed rather different from those of ZnP and ZnTPP. The peripheral substitution breaks the molecular D_4h symmetry of the porphyrin, thereby leading to the splitting of the absorption Q band. On the other hand, the B band in the spectra may not arise only from a single excited state; instead, it could be made up of several states that are close in energy. The calculated hyperpolarisabilities (β _vec) increase strongly from ZnPor 1 to ZnPor 2 to ZnPor3. The latter two molecules were predicted to have a large β _vec value and thus may have potential application in the development of nonlinear optical (NLO) materials.     

Energy transfer to an anharmonic diatomic system

We model an anharmonic diatomic molecule using deformed creation and annihilation operators such that the energy spectrum generated by a Hamiltonian of the harmonic oscillator's form written in terms of deformed operators is similar to that of a Morse potential. We construct an approximate time evolution operator and evaluate transition probabilities which are compared with those obtained by an expansion in a basis of Morse eigenfunctions. The algebraic results compare favorably with the numerical results.