Quantum ab initio

Such a quantum ab-initio approach was initially performed by Csizmadia et al. 

The general complementarity of sensitivities in cw and femtosecond spectroscopy has been anticipated by Zewail [66] and it is verified for the Naa molecule excited to its electronic B state (see Sect. 3.2.4). This system has already been studied in great detail by various experimental and theoretical techniques such as cw two-photon ionization spectroscopy [68-70], femtosecond pump probe spectroscopy at high intensities [29, 30, 71], quantum ab initio studies [72-74], two-dimensional simulations of the pseudorot at ional progressions in the cw absorption spectra [75-78], and, finally, three-dimensional simulations by means of empirical potential-energy surfaces (PESs) [79, 80]. 

For this, various 3d quantum ab initio simulations of the wave packet dynamics in Naa B are presented here and compared to ultrashort laser pump probe experiments. In addition to exact QD calculations, an a > proximate QD method is suggested to simulate the main features of a pump probe spectrum. The simulations provide satisfactory results in comparison to exact QD calculations. By means of these two methods it is possible to reproduce and to explain the different experimental pump probe spectra. The 310 fs oscillation in the femtosecond pump probe experiment [62, 81] can clearly be assigned to the Qs vibration, while the 3ps oscillation of the picosecond pump probe experiment [306, 379] is caused by a slow pseudorotational wave packet motion. 

Singh UC, Kollman PA (1986) A combined quantum ab initio mechanical and molecular mechanical method for carrying out simulations on complex molecular systems Applications to the CH3CI + Cr exchange reaction and gas phase protonation of polyethers. J Comput Chem 7 718-730... 

At the time the experiments were perfomied (1984), this discrepancy between theory and experiment was attributed to quantum mechanical resonances drat led to enhanced reaction probability in the FlF(u = 3) chaimel for high impact parameter collisions. Flowever, since 1984, several new potential energy surfaces using a combination of ab initio calculations and empirical corrections were developed in which the bend potential near the barrier was found to be very flat or even non-collinear [49, M], in contrast to the Muckennan V surface. In 1988, Sato [ ] showed that classical trajectory calculations on a surface with a bent transition-state geometry produced angular distributions in which the FIF(u = 3) product was peaked at 0 = 0°, while the FIF(u = 2) product was predominantly scattered into the backward hemisphere (0 > 90°), thereby qualitatively reproducing the most important features in figure A3.7.5. 

Detailed analyses of the above experiments suggest that the apparent steps in k E) may not arise from quantized transition state energy levels [110.111]. Transition state models used to interpret the ketene and acetaldehyde dissociation experiments are not consistent with the results of high-level ab initio calculations [110.111]. The steps observed for NO2 dissociation may originate from the opening of electronically excited dissociation chaimels [107.108]. It is also of interest that RRKM-like steps in k E) are not found from detailed quantum dynamical calculations of unimolecular dissociation [91.101.102.112]. More studies are needed of unimolecular reactions near tln-eshold to detennine whether tiiere are actual quantized transition states and steps in k E) and, if not, what is the origin of the apparent steps in the above measurements of k E). 

The approach is ideally suited to the study of IVR on fast timescales, which is the most important primary process in imimolecular reactions. The application of high-resolution rovibrational overtone spectroscopy to this problem has been extensively demonstrated. Effective Hamiltonian analyses alone are insufficient, as has been demonstrated by explicit quantum dynamical models based on ab initio theory [95]. The fast IVR characteristic of the CH cliromophore in various molecular environments is probably the most comprehensively studied example of the kind [96] (see chapter A3.13). The importance of this question to chemical kinetics can perhaps best be illustrated with the following examples. The atom recombination reaction... 

As a scientific tool, ab initio quantum chemistry is not yet as accurate as modem laser spectroscopic measurements, for example. Moreover, it is difficult to estimate the accuracies with which various methods predict bond energies and lengths, excitation energies and the like. In the opinion of tlie author, chemists who... 

C) All mean-field models of electronic. structure require large corrections. Essentially all ab initio quantum chemistry approaches introduce a mean field potential F that embodies the average interactions among the electrons. The difference between the mean-field potential and the true Coulombic potential is temied [20] the "fluctuationpotentiar. The solutions Ef, to the true electronic... 

The mean-field potential and the need to improve it to aohieve reasonably aeourate solutions to the true eleotronio Selirodinger equation introduoe three oonstniots that oharaoterize essentially all ab initio quantum ohemioal methods orbitals, configurations and electron correlation. 

In most of the connnonly used ab initio quantum chemical methods [26], one fonns a set of configurations by placing N electrons into spin orbitals in a maimer that produces the spatial, spin and angular momentum syimnetry of the electronic state of interest. The correct wavefimction T is then written as a linear combination of tire mean-field configuration fimctions qj = example, to describe the... 

In most ab initio quantum ehemieal methods, the eorrelation ealeulation is aetiially earried out by fonning a linear eombination of the mean-field eonfiguration state funetions and detemiining the C ] amplitudes by some proeediire. The identities diseussed hr some detail above are then introdueed merely to pemrit one to interpret the presenee of eonfigurations that are doubly exeited relative to the dominant mean-field eonfiguration in temrs of polarized orbital pairs. 

The simplest trial fiinction employed in ab initio quantum chemistry is the single Slater detemiinant fiinction in which N spin orbitals are occupied by N electrons ... 

First-principles models of solid surfaces and adsorption and reaction of atoms and molecules on those surfaces range from ab initio quantum chemistry (HF configuration interaction (Cl), perturbation theory (PT), etc for details see chapter B3.1 ) on small, finite clusters of atoms to HF or DFT on two-dimensionally infinite slabs. In between these... 

Flammond B L, Lester W A and Reynolds P J 1994 Monte Cario Methods in Ab initio Quantum Chemistry (Singapore World Scientific)... 

Pisani C (ed) 1996 Quantum-Mechanicai Ab-initio Caicuiation of the Properties of Crystaiiine Materiais (Lecture Notes in Chemistry voi 67) (Beriin Springer)... 

Car and Parrinello [202] proposed a teclmique for efficiently solving the Scluodinger equation which has had an enonuous impact on materials simulation (for reviews, see [203. 204. 205. 206]). The technique is an ab initio one, i.e., free of empirical parameters, and is based on the use of a quantum mechanical orthononual... 

Truong T N 1997 Thermal rates of hydrogen exchange of methane with zeolite a direct ab initio dynamics study on the importance of quantum tunneling effects J. Rhys. Chem. B 101 2750... 

An excellent, up-to-date treatise on geometry optimization and reaction path algorithms for ab initio quantum chemical calculations, including practical aspects. 

Smalley R E 1985 Supersonic cluster beams an alternative approach to surface science Comparison of Ab Initio Quantum Chemistry with Experiment for Small Molecules ed R J Bartlett (Boston Reldel)... 

A further model Hamiltonian that is tailored for the treatment of non-adiabatic systems is the vibronic coupling (VC) model of Koppel et al. [65]. This provides an analytic expression for PES coupled by non-adiabatic effects, which can be fitted to ab initio calculations using only a few data points. As a result, it is a useful tool in the description of photochemical systems. It is also very useful in the development of dynamics methods, as it provides realistic global surfaces that can be used both for exact quantum wavepacket dynamics and more approximate methods. 

The gradient of the PES (force) can in principle be calculated by finite difference methods. This is, however, extremely inefficient, requiring many evaluations of the wave function. Gradient methods in quantum chemistiy are fortunately now very advanced, and analytic gradients are available for a wide variety of ab initio methods [123-127]. Note that if the wave function depends on a set of parameters X], for example, the expansion coefficients of the basis functions used to build the orbitals in molecular orbital (MO) theory. 

The adiabatic picture is the standard one in quantum chemistry for the reason that, not only is it mathematically well defined, but it is also that used in ab initio calculations, which solve the electronic Hamiltonian at a particular nuclear geometry. To see the effects of vibronic coupling on the potential energy surfaces one must move to what is called a diabatic representation [1,65,180, 181]. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

As ab initio MD for all valence electrons [27] is not feasible for very large systems, QM calculations of an embedded quantum subsystem axe required. Since reviews of the various approaches that rely on the Born-Oppenheimer approximation and that are now in use or in development, are available (see Field [87], Merz ]88], Aqvist and Warshel [89], and Bakowies and Thiel [90] and references therein), only some summarizing opinions will be given here. 

The second aspect, predicting reaction dynamics, including the quantum behaviour of protons, still has some way to go There are really two separate problems the simulation of a slow activated event, and the quantum-dynamical aspects of a reactive transition. Only fast reactions, occurring on the pico- to nanosecond time scale, can be probed by direct simulation an interesting example is the simulation by ab initio MD of metallocene-catalysed ethylene polymerisation by Meier et al. [93]. 

Abstract. We present novel time integration schemes for Newtonian dynamics whose fastest oscillations are nearly harmonic, for constrained Newtonian dynamics including the Car-Parrinello equations of ab initio molecular dynamics, and for mixed quantum-classical molecular dynamics. The methods attain favorable properties by using matrix-function vector products which are computed via Lanczos method. This permits to take longer time steps than in standard integrators. 

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