Energy Subtraction

An alternative formulation of QM/MM is the energy subtraction method. In this method, calculations are done on various regions of the molecule with 

---

Correct the base energy by including diffuse functions on a second ener calculation by computing the MP4/6-31 lG+(d,p) energy. Subtract the ba... 

Correct the base energy with higher polarization functions on heavy ator by computing the MP4/6-311G(2df,p) energy. Subtract E from tf energy to obtain If AE is positive (meaning the addition... 

Correct the base energy for residual correlation effects (to countera known deficiencies of truncating perturbation theory at fourth order) 1 computing the QCISD(T)/6-311G(d,p) energy. Subtract E from th energy to produce AE ... 

Dimensionless amplitude, 141 Directional bremsstrahlung, 131 Displacive excitation of coherent phonons (DECP), 27, 56 Dissociative attachment, 103 Double plasma mirror (DPM), 194 Dual energy subtraction imaging, 178... 

Figure 4.12 Photoionization spectrum of HeO1 S) between the thresholds for He+(n = 4) and He+(n = 6). Dots Experiment [126]. Curve Hyperspherical close-coupling calculations convoluted with an experimental energy resolution of 6 meV and the background linear in photon energy subtracted. This background is caused mostly by the decay of the electron current in the storage ring. Figure from Ref. [51].

Since F = fi + N/j. — f n(r)u(r)dr, F is identified as the intrinsic (Helmholtz) free energy, i.e. the free energy with external field energy subtracted out. 

Figure 7.11. Upper panels show spin spirals with relaxed moments for two different lattice parameters. Bottom panels show the magnetization energy of fixed moment spin spirals with the intrasite exchange energy subtracted.

Quasi-relativistic approximations usually start from re-writing the Dirac equation in two-component form. Starting from the Dirac equation (with rest energy subtracted)... 

Since there are two electrons per MO, the quantity 2 e, is the sum of the orbital energies. Subtraction of the double sum in (13.155) avoids counting each interelec-tronic repulsion twice, as discussed in Section 11.1. 

This is the equation for the conservation of total energy. Subtracting the mechanical energy equation (6.9.2) from equation (6.11.2) gives the thermal energy equation... 

---