Exploring potential energy surfaces for chemical reactions: an overview of some practical methods

Potential energy surfaces form a central concept in the application of electronic structure methods to the study of molecular structures, properties, and reactivities. Recent advances in tools for exploring potential energy surfaces are surveyed. Methods for geometry optimization of equilibrium structures, searching for transition states, following reaction paths and ab initio molecular dynamics are discussed. For geometry optimization, topics include methods for large molecules, QM/MM calculations, and simultaneous optimization of the wave function and the geometry. Path optimization methods and dynamics based techniques for transition state searching and reaction path following are outlined. Developments in the calculation of ab initio classical trajectories in the Born-Oppenheimer and Car-Parrinello approaches are described.     

On the origin of dynamic instability of molecular systems

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH₃, planar square CH₄ and linear H ₃ ⁺ ) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.     

Clusters,metastability, and nucleation: Kinetics of first-order phase transitions

We describe and interpret computer simulations of the time evolution of a binary alloy on a cubic lattice, with nearest neighbor interactions favoring like pairs of atoms. Initially the atoms are arranged at random; the time evolution proceeds by random interchanges of nearest neighbor pairs, using probabilities compatible with the equilibrium Gibbs distribution at temperatureT. For temperatures 0.59T_c, 0.81 T_c, and 0.89T _c, with density of A atoms equal to that in the B-rich phase at coexistence, the density C₁ of clusters ofl A atoms approximately satisfies the following empirical formulas: C₁ w(1 –)³ andC ₁, (1 –)⁴Q₁w¹ (2 l 10). Herew is a parameter and we defineQ _l = _K e ^–E(K) , where the sum goes over all translationally nonequivalentl-particle clusters andE(K) is the energy of formation of the clusterK. Forl > 10,Q ₁ is not known exactly; so we use an extrapolation formulaQ _l Aw _s ^–l l ^– exp(–bl ), wherew _s is the value ofw at coexistence. The same formula (withw > w _s) also fits the observed values of C, (for small values ofl) at densities greater than the coexistence density (forT=0.59T_c): When the supersaturation is small, the simulations show apparently metastable states, a theoretical estimate of whose lifetime is compatible with the observations. For higher supersaturation the system is observed to undergo a slow process of segregation into two coexisting phases (andw therefore changes slowly with time). These results may be interpreted as a more quantitative formulation (and confirmation) of ideas used in standard nucleation theory. No evidence for a spinodal transition is found.Supported by AFOSR Grant No. 73-2430D and by ERDA Contract No. EY-76-C-02-3077*000.     

A theoretical study of the lowest electronic states of azobenzene: the role of torsion coordinate in the cis–trans photoisomerization

In the present paper we report the results of a multiconfigurational computational study on potential-energy curves of azobenzene along the NN twisting to clarify the role of this coordinate in the decay of the S₂(*) and S₁(n*) states. We have found that there is a singlet state, S₃ at the trans geometry, on the basis of the doubly excited configuration n²*², that has a deep minimum at about 90° of twisting, where it is the lowest excited singlet state. The existence of this state provides an explanation for the short lifetime of S₂(*) and for the wavelength-dependence of azobenzene photochemistry. We have characterized the S₁(n*) state by calculating its vibrational frequencies, which are found to correspond to the recently observed transient Raman spectrum. We have also computed the potential-energy curve for the triplet T₁(n*) at the density functional theory B3LYP level, which indicates that in this state the isomerization occurs along the twisting coordinate.Acknowledgement The financial support from MIUR (project Modellistica delle proprietà spettroscopiche di sistemi molecolari complessi funds ex 60% and project Dinamiche molecolari in sistemi di interesse chimico funds ex 40%), from the University of Bologna (Funds for Selected Research Topics) is gratefully acknowledged.Contribution to the Jacopo Tomasi Honorary Issue     

A comparative study on the photochemistry of two bipyridyl derivatives: [2,2'-bipyridyl]-3,3'-diamine and [2,2'-bipyridyl]-3,3'-diol.

The two isoelectronic bipyridyl derivatives, [2,2'-bipyridyl]-3,3'-diamine and [2,2'-bipyridyl]-3,3'-diol, are experimentally known to undergo very different excited-state double-proton-transfer processes, which result in fluorescence quantum yields that differ by four orders of magnitude. Herein, density functional theory (DFT), time-dependent DFT (TDDFT), and complete active space self-consistent field (CASSCF) calculations are used to study the double-proton-transfer processes in the ground and first singlet pi-->pi* excited state. The quantum-chemistry calculations indicate 1) the existence of only one energy minimum in the ground electronic state corresponding to reactants (thus avoiding the possibility of a fast fluorescent relaxation process from the photoproducts region), 2) an endoergic process of the complete double proton transfer, and 3) the presence of a conical intersection in the excited intermediate region of [2,2'-bipyridyl]-3,3'-diamine. These facts explain the very low fluorescence quantum yield in [2,2'-bipyridyl]-3,3'-diamine compared to [2,2'-bipyridyl]-3,3'-diol.     

On the equation of state of classical one-component systems with long-range forces

Several definitions of the pressure are introduced for one-component systems and shown to be nonequivalent in the presence of a rigid neutralizing background. Relations between these pressures are derived for finite and infinite systems; these relations depend on the asymptotic behavior of the force at infinity, with the Coulomb force at the borderline between different properties. It is argued that only one of those definitions is physically acceptable and its properties are discussed in relation to the asymptotic behavior of the force. It is seen in particular that a knowledge of the state of the infinite system is not sufficient to determine its thermodynamic properties. The results are illustrated by some typical examples.For example, for two-dimensional systems with three-dimensional Coulomb interaction see refs. 2–4.     

Lower bounds on the cluster size distribution

We rigorously prove that the probabilityP _n that the origin of ad-dimensional lattice belongs to a cluster of exactlyn sites satisfiesP _n > exp(–n ^(d–1)/d ) whenever percolation occurs. This holds for the usual (noninteracting) percolation models for any concentrationp > p _c , as well as for the equilibrium states of lattice spin systems with quite general interactions. Such a lower bound applies also if no percolation occurs, but if it appears in some other phase of the system.     

A comparison of the mechanism for the reductive half-reaction between pea seedling and other copper amine oxidases (CAOs)

In a previous DFT study a mechanism for the reductive half-reaction of pea seedling amine oxidase (PSAO) was suggested. In many of the suggested steps a lysine at the active site plays an important role. However, this lysine is not found in other amine oxidases. The primary aim of the present DFT study is therefore to investigate alternative mechanisms for those amine oxidases (CAO) where the lysine residue is not present. One of the most important roles suggested for the lysine in PSAO was to protonate the O2-site of TPQ before the critical Cbond;H bond cleavage of the substrate. In the absence of lysine the O2-site of TPQ is now suggested to be protonated by a water ligand on the copper metal complex, in line with experimental suggestions. In other steps the role of lysine is taken over by an asparagine. All results are compared with experimental observations and good agreement is generally found.     

Emission band shape probes of the mixed-valence excited state properties of polypyridyl-bridged bis-ruthenium(II) complexes

The absorption spectra and emission spectral band shapes of several polypyridine-ligand (PP) bridged bis-ruthenium(II) complexes imply that the Ru(II)/Ru(III) electronic coupling is weak in their lowest energy metal to ligand charge transfer (MLCT) excited states. Many of these PP-bridging ligands contain pyrazine moieties and the weak electronic coupling of the excited states contrasts to the strong electronic coupling inferred for the correlated mixed-valence ground states. Although the bimetallic complexes emit at significantly lower energy than their monometallic analogs, the vibronic contributions to their 77 K emission spectra are much stronger than expected based on comparison to the monometallic analogs (around twofold in some complexes) and this feature is characteristic of bimetallic complexes in which the mixed-valence excited states are electronically localized. The weaker excited state than ground state donor/acceptor electronic coupling in this class of complexes is attributed to PP-mediated super-exchange coupling in which the mediating orbital of the bridging ligand (PP-LUMO) is partly occupied in the MLCT excited states, but is unoccupied in the ground states; therefore, the vertical Ru(III)-PP⁻ (MLCT) energy is larger and the mixing coefficient smaller in these excited states than is found for Ru(II)-PP in the corresponding ground states.     

UHF-AM1 studies on 1,4 and 1,5 intramolecular H-atom transfer reactions in alkenyl radicals

The transition states of intramolecular 1,4 and 1,5 H-atom transfers, from/to primary (p), secondary (s) or tertiary alkyl (t) and primary (p _a), secondary (s _a) or tertiary (t _a) allyl carbon atoms, have been studied at the level of the semiempirical quantum-chemical method AM1 with the UHF approximation. The activation and reaction enthalpies were calculated and compared with experimental data available in the literature and the calculated data obtained for analogous reactions in alkyl radicals. Correlations were found between the activation enthalpies and the dissociation enthalpies of the bonds broken and formed.