Quantum simulations

Gillan M J 1987 Quantum simulation of hydrogen in metals Phys. Rev. Lett. 58 563... 

With the rapid development of computer power, and the continual hmovation of simulation methods, it is impossible to predict what may be achieved over the next few years, except to say that the outlook is very promising. The areas of rare events, phase equilibria, and quantum simulation continue to be active. 

Rossky, P.J., Schnitker, J. The hydrated electron quantum simulation of structure, spectroscopy and dynamics. J. Phys. Chem. 92 (1988) 4277-4285. 

Berendsen, H.J.C., Mavri, J. Quantum simulation of reaction dynamics by Density Matrix Evolution. J. Phys. Chem. 97 (1993) 13464-13468. 

Two methods for time-dependent quantum simulations of many-atom systems are examined in this article the CSP-based and the Cl-CSP-based algorithms. The CSP method begins with a separable approximation for... 

The full ab-initio molecular dynamics simulation revealed the insertion of ethylene into the Zr-C bond, leading to propyl formation. The dynamics simulations showed that this first step in ethylene polymerisation is extremely fast. Figure 2 shows the distance between the carbon atoms in ethylene and between an ethylene carbon and the methyl carbon, from which it follows that the insertion time is only about 170 fs. This observation suggests the absence of any significant barrier of activation at this stage of the polymerisation process, and for this catalyst. The absence or very small value of a barrier for insertion of ethylene into a bis-cyclopentadienyl titanocene or zirconocene has also been confirmed by static quantum simulations reported independently... 

In modern materials science topics of high interest are surface structures on small (nanometer-length) scales and phase transitions in adsorbed surface layers. Many interesting effects appear at low temperatures, where quantum effects are important, which have to be taken into account in theoretical analyses. In this review a progress report is given on the state of the art of (quantum) simulations of adsorbed molecular layers. 

Other quantum simulations involve simulations with effective Hamiltonians [261-263] or the simulation of ground state wave properties by Green s function Monte Carlo or diffusion Monte Carlo for reviews and further references on these methods see Refs. 162, 264-268. 

Furthermore, one can infer quantitatively from the data in Fig. 13 that the quantum system cannot reach the maximum herringbone ordering even at extremely low temperatures the quantum hbrations depress the saturation value by 10%. In Fig. 13, the order parameter and total energy as obtained from the full quantum simulation are compared with standard approximate theories valid for low and high temperatures. One can clearly see how the quasi classical Feynman-Hibbs curve matches the exact quantum data above 30 K. However, just below the phase transition, this second-order approximation in the quantum fluctuations fails and yields uncontrolled estimates just below the point of failure it gives classical values for the order parameter and the herringbone ordering even vanishes below... 

FIG. 13 Herringbone order parameter and total energy for N2 (X model with Steele s corrugation). Quantum simulation, full line classical simulation, dotted line quasiharmonic theory, dashed line Feynman-Hibbs simulation, triangles. The lines are linear connections of the data. (Reprinted with permission from Ref. 95, Fig. 4. 1993, American Physical Society.)... 

J. D. Doll, J. E. Gubematis, eds. Quantum Simulation of Condensed Matter Phenomena. Singapore World Scientific, 1990. 

A more practical approach for larger systems is molecular dynamics. In this method, the properties of bonds are determined through a combination of quantum-mechanical simulation and physical experiments, and stored in a database called a (semi-empirical) force field. Then a classical (non-quantum) simulation is done where bonds are modeled as spring-like interactions. Molecular... 

The approach to the evaluation of vibrational spectra described above is based on classical simulations for which quantum corrections are possible. The incorporation of quantum effects directly in simulations of large molecular systems is one of the most challenging areas in theoretical chemistry today. The development of quantum simulation methods is particularly important in the area of molecular spectroscopy for which quantum effects can be important and where the goal is to use simulations to help understand the structural and dynamical origins of changes in spectral lineshapes with environmental variables such as the temperature. The direct evaluation of quantum time- correlation functions for anharmonic systems is extremely difficult. Our initial approach to the evaluation of finite temperature anharmonic effects on vibrational lineshapes is derived from the fact that the moments of the vibrational lineshape spectrum can be expressed as functions of expectation values of positional and momentum operators. These expectation values can be evaluated using extremely efficient quantum Monte-Carlo techniques. The main points are summarized below. 

Since CASSCF calculations are necessary to obtain accurate excitation energies the examination of a large number of snapshots would be intractable. The MD/QM methodology instead allows the use of a few, carefully chosen representative structures for which to carry quantum simulations. 

This section describes the main methodological advances that will be used in subsequent selected applications, including (1) Development of fast semiempirical methods for multiscale quantum simulations, (2) Directions for development of next-generation QM/MM models, and (3) Linear-scaling electrostatic and generalized solvent boundary methods. 

Development of Fast Semiempirical Methods for Multiscale Quantum Simulations... 

The use of trapped ions, or trapped atoms, as qubits [46, 47] is one of the most mature techniques. They have been used to achieve remarkable feats, mainly in the field of quantum simulation [48]. However, there is no clear link between this technology and molecular systems. 

The results of the quantum simulations for cases A, B and C are shown in the lower two panels in Fig. 3. The corresponding classical phase portraits shown reinforce our inferences from the stability diagram no stabilization for A while larger islands exist for C as compared with B. However, the ionized fraction as calculated from the quantum evolution supports the contrary result that there is more stabilization for A as compared with B. Case C is the most stable which is at least consistent with the classical prediction. What is the origin of this discrepancy ... 

Roberto Dovesi, Bartolomeo Civalleri, Roberto Orlando, Carla Roetti and Victor R. Saunders, Ab Initio Quantum Simulation in Solid State Chemistry. 

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