Computing on the fly

After the requisite integrals are available or are being computed on the fly, to begin the SCE process one must input into the computer routine which computes F the initial guesses for the C. values corresponding to... 

Once the controller (a computer) evaluates these two manipulated variables, it also computes on the fly the actual signals necessary for the two mass flow rates nij and m2. The computation... 

Another major, future advance in the quantum chemical computation of potential energy surfaces for reaction dynamics will be the ability to routinely compute the energies of molecular systems on the fly . The tedious and time-consuming process of fitting computed quantum chemical values to functional forms could be avoided if it were possible to compute the PES as needed during a classical trajectory or quantum dynamics calculation. For many chemical reactions, it should be practical in the near future to prudently select a sufficiently rapid and accurate electronic structure method to facilitate dynamics computations on the fly. 

More commonly, s are computed on the fly by computer programs as part of an equilibrium speciation calculation. These programs employ various numerical approaches for estimating K, such as the one shown in Eq. 5.11. In this case, the... 

A closer relationship between EVB and QM/MM is apparent when some components of the matrix elements are computed on the fly at a quantum mechanical level. Mo and Gao (2000), for instance, have described such a technique in the absence of an MM region where an EVB Hamiltonian that includes QM-computed terms is coupled with a surrounding QM region in a non-SCF fashion. The extension of this melhodology to include an MM region follows naturally from the QM/MM couplings described above. 

The C and D coefficients are parameters fitted to reproduce a set of experimental dipole moments. The atomic CM3 charges are conformationally dependent. They can either be averaged over a number of representative conformations and fixed, or computed on the fly for example, in the course of MD simulations. 

As noted above, the density-of-states method described earlier can be extended to yield accurate estimates of the potential of mean force. The weight factors that dictate the walk in the space can be computed on the fly during a simulation in a self-consistent manner. The simulation can be performed without any constraints, which means that the resulting weights can be used directly as in (21) to give the potential of mean force. One can also accumulate the forces acting on the particles that define the reaction coordinate and then use (24) to get the PMF. The computed PMF is therefore available as a continuous function of... 

Twenty years ago Car and Parrinello introduced an efficient method to perform Molecular Dynamics simulation for classical nuclei with forces computed on the fly by a Density Functional Theory (DFT) based electronic calculation [1], Because the method allowed study of the statistical mechanics of classical nuclei with many-body electronic interactions, it opened the way for the use of simulation methods for realistic systems with an accuracy well beyond the limits of available effective force fields. In the last twenty years, the number of applications of the Car-Parrinello ab-initio molecular d3mam-ics has ranged from simple covalent bonded solids, to high pressure physics, material science and biological systems. There have also been extensions of the original algorithm to simulate systems at constant temperature and constant pressure [2], finite temperature effects for the electrons [3], and quantum nuclei [4]. 

In order to perform ah initio molecular dynamics in excited states, the forces on the atoms are computed on the fly. There are two different implementations of force calculations for the two TDDFT schemes, P-TDDFT and LR-TDDFT. In the first case, the excited state is obtained with the promotion of one electron from the highest occupied molecular orbital (HOMO) to a selected unoccupied molecular orbital (the lowest one, LUMO, in our case). The corresponding KS excited single-determinant configuration is taken for the computation of the electronic density, which is then used to compute the forces on the atoms according to the Hellmann-Feynman electrostatic theorem [35]... 

The opposite extreme — adopted by biochemists studying extremely large systems such as proteins — is to carry out the dynamics relying on classical mechanics methods only. The energy and first derivatives of the potential-energy surface (i.e., force constants) are computed on-the-fly using force-field methods (i.e., molecular mechanics [MM]) and are passed... 

In practical Monte Carlo settings, the shift Er is computed on the fly and consequently is a slowly varying, nearly constant function of time, but for the moment we take it to be constant. The wavefunction i (R, 0 is the solution to the Schrodinger equation in imaginary time... 

Within this approach, the spectroscopic parameters can either be computed on the fly or, more frequently, by accurate single-point calculations on different static cluster configurations extracted from the molecular dynamic (MD) trajectory [56]. A disadvantage of the approach is that the lack of a representative unperturbed reference geometry does not allow to isolate the different normal-mode contributions to the computed molecular property. 

In practical appUcations, will not be stored as such, but will be computed on the fly from (c/ section 3.4.2) with the trivial operations ... 

The QM/MM Hamiltonian can be used to cany out Molecular Dynamics simulations of a complex system. In the case of liquid interfaces, the simulation box contains the solute and solvent molecules and one must apply appropriate periodic boundary conditions. Typically, for air-water interface simulations, we use a cubic box with periodic boundary conditions in the X and Y directions, whereas for liquid/liquid interfaces, we use a rectangle cuboid interface with periodic boundary conditions in the three directions. An example of simulation box for a liquid-liquid interface is illustrated in Fig. 11.1. The solute s wave function is computed on the fly at each time step of the simulation using the terms in the whole Hamiltonian that explicitly depend on the solute s electronic coordinates (the Born-Oppenheimer approximation is assumed in this model). To accelerate the convergence of the wavefunction calculation, the initial guess in the SCF iterative procedure is taken from the previous step in the simulation, or better, using an extrapolated density matrix from the last three or four steps [39]. The forces acting on QM nuclei and on MM centers are evaluated analytically, and the classical equations of motion are solved to obtain a set of new atomic positions and velocities. 

Semiclassical Wave Packet Dynamics with Electronic Structure Computed on the Fly Application to Photophysics of Electronic Excited States in Condensed Phase. 

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