We present the theoretical and technical foundations of the Amsterdam Density Functional (ADF) program with a survey of the characteristics of the code (numerical integration, density fitting for the Coulomb potential, and STO basis functions). Recent developments enhance the efficiency of ADF (e.g., parallelization, near order-N scaling, QM/MM) and its functionality (e.g., NMR chemical shifts, COSMO solvent effects, ZORA relativistic method, excitation energies, frequency-dependent (hyper)polarizabilities, atomic VDD charges). In the Applications section we discuss the physical model of the electronic structure and the chemical bond, i.e., the Kohn–Sham molecular orbital (MO) theory, and illustrate the power of the Kohn–Sham MO model in conjunction with the ADF-typical fragment approach to quantitatively understand and predict chemical phenomena. We review the “Activation-strain TS interaction” (ATS) model of chemical reactivity as a conceptual framework for understanding how activation barriers of various types of (competing) reaction mechanisms arise and how they may be controlled, for example, in organic chemistry or homogeneous catalysis. Finally, we include a brief discussion of exemplary applications in the field of biochemistry (structure and bonding of DNA) and of time-dependent density functional theory (TDDFT) to indicate how this development further reinforces the ADF tools for the analysis of chemical phenomena. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 931–967, 2001

Chemistry with ADF

The problem of determining which activated (and slow) transitions can occur from a given initial state at a finite temperature is addressed. In the harmonic approximation to transition state theory this problem reduces to finding the set of low lying saddle points at the boundary of the potential energy basin associated with the initial state, as well as the relevant vibrational frequencies. Also, when full transition state theory calculations are carried out, it can be useful to know the location of the saddle points on the potential energy surface. A method for finding saddle points without knowledge of the final state of the transition is described. The method only makes use of first derivatives of the potential energy and is, therefore, applicable in situations where second derivatives are too costly or too tedious to evaluate, for example, in plane wave based density functional theory calculations. It is also designed to scale efficiently with the dimensionality of the system and can be applied to very large systems when empirical or semiempirical methods are used to obtain the atomic forces. The method can be started from the potential minimum representing the initial state, or from an initial guess closer to the saddle point. An application to Al adatom diffusion on an Al(100) surface described by an embedded atom method potential is presented. A large number of saddle points were found for adatom diffusion and dimer/vacancy formation. A surprisingly low energy four atom exchange process was found as well as processes indicative of local hex reconstruction of the surface layer.

A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives

Kohn-Sham Density Functional Theory: Predicting and Understanding Chemistry

We present a method for carrying out long time scale dynamics simulations within the harmonic transition state theory approximation. For each state of the system, characterized by a local minimum on the potential energy surface, multiple searches for saddle points are carried out using random initial directions. The dimer method is used for the saddle point searches and the rate for each transition mechanism is estimated using harmonic transition state theory. Transitions are selected and the clock advanced according to the kinetic Monte Carlo algorithm. Unlike traditional applications of kinetic Monte Carlo, the atoms are not assumed to sit on lattice sites and a list of all possible transitions need not be specified beforehand. Rather, the relevant transitions are found on the fly during the simulation. A multiple time scale simulation of Al(100) crystal growth is presented where the deposition event, occurring on the time scale of picoseconds, is simulated by ordinary classical dynamics, but the time i...

Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table

Publisher Summary Single electron transfer to or from molecules is often accompanied by other reactions involving the formation or the cleavage of bonds. The high energy intermediates thus formed can undergo further electron transfer with the same electron source or sink that initiated the reaction. Among the reactions accompanying electron transfer, bond breaking is a common mode by which a free radical and a diamagnetic leaving group are produced by single electron transfer to a diamagnetic molecule. Such reactions bridge single electron-transfer chemistry and radical chemistry. This chapter explores how the dynamics of concerted electron-transfer/bond-breaking reactions can be modeled and the contribution of bond breaking to the activation barrier. It discusses thermal heterogeneous and homogeneous reactions and molecular parameters that govern the concerted/stepwise dichotomy. The dynamics of the cleavage and coupling reactions and the electron transfer/bond breaking process are examined. Most investigations of dissociative electron transfer concerns thermal reactions and photoinduced-dissociative electron transfer. Quantum yield expressions for the concerted and stepwise cases are established and experimental examples are discussed.

Electron transfer, bond breaking, and bond formation

Structures and stabilities of singly charged three-electron hemibonded systems and their hydrogen-bonded isomers

A branching point is a point on a reaction path leading from reactants to products (via a transition state) at which it is energetically favorable for the system to break symmetry. Such a point can be defined in terms of normal modes along the reaction path and corresponds to zero curvature (a zero Hessian eigenvalue) along a symmetry-breaking mode. An effective method for the location of such points is presented and realized in an efficient, practical algorithm designed for use in the ab initio program package Gaussian 82.

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An algorithm for the location of branching points on reaction paths

A detailed study of the mechanism by which a proton is lost from a dication reveals that such processes are more complicated than is often assumed. In many cases, a deprotonation reaction is best viewed as a two-stage process: Initially, the departing unit is better described as a hydrogen atom than as a proton and only later, at some point further along the decomposition pathway, does a spontaneous electron transfer take place to form the eventual products. Consequently, it is found that, contrary to conventional wisdom, restricted Hartree-Fock (RHF) theory does not necessarily offer a satisfactory theoretical treatment of such fragmentations. The circumstances under which it is appropriate to use RHF or UHF procedures (and the M0ller-Plesset perturbation theories based on these) are examined in light of a recent model for dication dissociation, and it is found that the A parameter of that model is a useful aid in choosing the theoretical formalism appropriate to a given dication. The chemistry of gas-phase dications has received considerable attention in recent years, from both theoreticians and experi- mentalists.' Such species

How Does a Dication Lose a Proton

Ab initio molecular orbital theory has been used in a systematic study of the firstand second-row dimer dications He?+, H3NNH32+, H200H22+, HFFH", Ne22+, H3PPH32+, H2SSH22+, HC1C1H2+, and Ar22+. Although all nine systems are thermodynamically unstable with respect to symmetric fragmentation into two monocations, potential energy barriers inhibiting such fragmentations are predicted to exist for all of the dimers except HFFH2+, Ne?+, and Ar22+. In particular, the hydrazinium and diphosphinium dications are found to be very stable kinetically with respect to both symmetric fragmentation and deprotonation. The equilibrium A-A bond lengths in the dimer dications (A?') are all significantly shorter than in the corresponding (hemibonded) monocations (A2'+), but the fragmentation barriers are usually smaller. The equilibrium structures of the dimer dications are found to be very similar to those of their isoelectronic, isostructural, neutral counterparts. The usefulness of the recently introduced A parameter in understanding the stabilities and fragmentation processes of all nine dications is emphasized. The chemistry of gas-phase dications is progressing rapidly on both theoretical and experimental fronts.' Because the total nuclear (positive) charge in such ions exceeds the total electronic (negative) charge by two electronic units, there is a very strong tendency, in almost all of these systems, for a "coulomb explosion" to occur, leading to the formation of two monocations. Despite this, many dications are metastable species whose lifetimes are sufficiently great that they may be studied experimentally. Indeed, some are even thermodynamically stable; that is, they are lower in energy than any of their possible fragmentation products and are therefore indefinitely stable in isolation. In a previous study,2 we have investigated the family of three-electron hemibonded A2*+ dimers where A is one of the normal-valent hydrides He, NH3, H 2 0 , HF, Ne, PH3, HIS, HCI, or Ar and in which the monomeric units are bonded through the heavy atoms. We have found that the hemibond strengths in such species are remarkably strong (>IO0 kJ mol-]). The formation of stable monocations of this type is not unexpected because, in ionizing a neutral A, dimer, an electron is removed from an antibonding orbital, leading to the formation of a three-electron bond (Figure 1). For example, ionization in the He2 system changes a repulsive four-electron interaction in neutral He2 to a bonding three-electron interaction (with a formal bond order of in He;+. It is natural then to inquire whether the removal of a second antibonding electron, leading to the formation of a dicationic A?+ dimer, will lead to an even stronger A-A bond (with, a formal bond order of unity, Figure 1). Although it is likely that, in some of the dications, the enhanced covalent binding may be partially offset by the substantial coulombic repulsion, which will be present in such species, the counterintuitive theoretical finding that a bond may be strengthened by effective charges on the adjacent n ~ c l e i , ~ and the fact that both the He22+ dication4 and the N2H62+ dication5 have already been observed experimentally, encouraged us to undertake a detailed study of the complete family of A22+ dimers (where A is one of the normal-valent firstor second-row hydrides, as above). Some of the main properties of the A2*+ dimer dications, e.g. their equilibrium structures, would be expected to be well described by conventional theoretical procedures. On the other hand, it is ~ e l l k n o w n ~ * ~ that the theoretical study of the fragmentation of (1 ) For a recent review, see: Koch, W.; Schwarz, H. Structure/Reactiuity and Thermochemistry of Ions; Lias, S. G., Ausloos, P., Eds.; Reidel: Dordrecht, The Netherlands, 1987. (2) Gill, P. M. W.; Radom, L. J . Am. Chem. SOC. 1988, 110, 4931. (3) Dunitz, J . D.; Ha, T. K. J . Chem. Soc., Chem. Commun. 1972, 568. (4) Guilhaus, M.; Brenton, A. G.; Beynon, J. H.; Rabrenovic, M.; Schleyer, P. v. R. J . Phys. B 1984, 17, L605. ( 5 ) See, for example: Frlec, B.; Gantar, D.; Golic, L.; Leban, I. Acta Crystallogr. 1981, 37, 666. (6) Schleyer, P. v. R. Adu. Mass. Spectrom. 1985, 287. (7) See, for example: Taylor, P. Mol. Phys. 1983, 49, 1297. Table I. Basis Set Dependence of the Calculated Equilibrium Bond Length (rq, A), Transition Structure Bond Length (rn, A), Dissociation Barrier (De*, k J mol-I), and A Value (kJ mol-I) for the Dication" basis set r, rm De' Ab STO-3G 3-2 1 G 6-31G 6-311G (1 0 s ) d 6-31 lG(d,p)' 6-31 lG(MC)(d,p)' 6-31 lG(MC)(d,2p)' 6-31 lG(MC)(d,3p)' 6-31 lG(MC)(d,3pd)'a 6-31 lG(MC)(d,3~2dYg 6-31 lG(MC)(d,3~2dlf)'-"

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Structures and stabilities of the dimer dications of first- and second-row hydrides

The use of ab initio molecular orbital theory with moderately large basis sets and incorporation of electron correlation to study multiply-charged ions is discussed. Despite extreme coulomb repulsion, several of the ions have very short bonds. The C-F lengths in HCF2+ (I. 1 I1 A) and HeCF3' (1.102 A) and the C-CI length in HCCI" (1.466 A) are the shortest known for these types of bonds. Some of the more highly charged ions which have been examined, including the HeCF3+ and CHe;'' trications and the CHe:' tetracation, are predicted to be observable species, despite the possibility of highly exothermic (by -1000 kJ mol-' and more) fragmentations. It is found that unrestricted Moller-Plesset perturbation theory is not a suitable procedure for examining the fragmentation of multiply-charged ions in cases where spin contamination is significant in the underlying unrestricted HartreeFock wavefunction. Transition structures for asymmetric fragmentations of multiply-charged ions often occur late on the reaction pathway, with the length of the breaking bond hvo or more times greater than its value in the corresponding equilibrium structures.

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Peter M. W. Gill

Papers

Structures and stabilities of singly charged three-electron hemibonded systems and their hydrogen-bonded isomers

An algorithm for the location of branching points on reaction paths

How Does a Dication Lose a Proton

Structures and stabilities of the dimer dications of first- and second-row hydrides

Multiply-charged cations: remarkable structures and stabilities