Sum method

B. A. Luty, I. G. Tironi, and W. F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103 3014-3021, 1995. 

U. Essmann, L. Perera, M. L. Berkowitz, T. Darden, H. Lee, and L. G. Pedersen. The smooth particle mesh ewald method. J. Chem. Phys., 103 8577, 1995. Brock A. Luty, Ilario G. Tironi, and Wilfried F. van Gunsteren. Lattice-sum methods for calculating electrostatic interactions in molecular simulations. J. Chem. Phys., 103 3014-3021, 1995. 

Internal consistency among enthalpy values can also be judged without estimating absolute enthalpies using the oxide summing method. Finch and co-workers (89) obtained the following enthalpy values (kJ mol-1) for solids ... 

There are problems with using both of these methods in the simulation of inhomogeneous systems. Because the periodicity of the system is lost in the direction normal to the interface (unless one uses image charges with the flat wall model, which effectively results in a 3D periodic system implementation of the ES method is not straightforward for certain type of systems. Hautman and Klein have presented a modified Ewald sum method for the simulation of systems that are periodic in two... 

Gonzales-Platas, J., Gonzales-Silgo, C., and Ruis-Perez, C. (1999). VALMAP2-0 Contour maps using the bond-valence-sum method. J. Appl. Cryst. 32, 341-4. 

The DFT values for the At state derive from the sum method or projection techniques presented in Section 14.4, and discussion of those values is deferred to that point. As for the 2 A state, although no experimental measurement is available, comparison to other... 

To provide a specific example of die method, near UV experiments have led to assignments of the vertical and adiabatic excitation energies for die I B PAg transition in A-diazene (HN=NH), where the Bg state is open-shell. Table 14.4 compares sum-method predictions at the UHF and BLYP levels of theory to diese experimental values, and also to published results at the MRCI level of theory. For diis system, die HF results are systematically too high, and the DFT too low (cf. the sum method prediction for A2 phenylnitrene in Table 14.1), but are competitive with the much more expensive MRCI results. Note that all three levels do quite well at predicting the difference in verdcal and adiabatic excitation energies. 

At the UHF level, the excitation energies from spin annihilation represent a fairly severe underestimation of the excited-state energies, and disagree significantly with the sum method results from that same level of theory. UHF spin annihilation is generally not a worthwhile method to apply unless spin contamination effects are fairly small, which obviously is not the case here. 

The largest drawback of the spin annihilation procedure is similar to that of the sum method. That is, while the spin-annihilated wave function which results from the application of Aj+i to the 50 50 antecedent is in principle spin pure, it is expressed in the MOs that were optimized for the 50 50 case. These MOs minimize the energy of the contaminated state, but not that of the spin pure state, and errors can be significant. Nevertheless, the speed of the sum and projection methods, and their utihty in many if not all instances, makes them useful for rough applications prior to resort to more expensive and sophisticated models. 

Figure 2.9 Estimation of osmotic pressure by the half-sum method...

I. Reda, J. Hickey, C. Long, D. Myers, T. Stoffel, S. Wilcox, J. J. Michalsky, E. G. Dutton, and D. Nelson, Using a blackbody to calculate net-longwave responsivity of shortwave solar pyranometers to correct for their thermal offset error during outdoor calibration using the component sum method, Journal of Atmospheric and Oceanic Technology 22 1531 (2005). 

J.N.L. Connor, W. Jakubetz, J. Manz, Exact quantum transition-probabilities by state path sum method—CoUinear F -F H2 reaction. Mot Phys. 29 (2) (1975) 347-355. 

Kraka and Cremer answered Hess criticisms by first arguing that the UB3LYP description of 42 includes appreciable triplet contamination. When this is corrected for using the sum method, the open ring isomer 42 is now more stable than 44. Furthermore, they note that Hess misassigned the experimental IR spectrum and there are actually only two bands in the 1200-1600 cm region. 

---