First-order coupling

In a similar fashion, a fraction of the velocity of the molecules with first-order coupling is transmitted to other molecules entangled with the latter. This is called second-order coupling (subscript 2). Still higher orders of effect radiate from the original molecule in the manner suggested by Fig. 2.13. Because of the... 

Equation (10.42) are the first-order Coupled Perturbed Hartree-Fock (CPHF) equations." The perturbed MO coefficients are given in terms of unperturbed quantities and the first-order Fock, Lagrange (a) and overlap matrices. The F term is given as (eq. (3.52)). 

In an early work by Mertz and Pettitt, an open system was devised, in which an extended variable, representing the extent of protonation, was used to couple the system to a chemical potential reservoir [67], This method was demonstrated in the simulation of the acid-base reaction of acetic acid with water [67], Recently, PHMD methods based on continuous protonation states have been developed, in which a set of continuous titration coordinates, A, bound between 0 and 1, is propagated simultaneously with the conformational degrees of freedom in explicit or continuum solvent MD simulations. In the acidostat method developed by Borjesson and Hiinenberger for explicit solvent simulations [13], A. is relaxed towards the equilibrium value via a first-order coupling scheme in analogy to Berendsen s thermostat [10]. However, the theoretical basis for the equilibrium condition used in the derivation seems unclear [3], A test using the pKa calculation for several small amines did not yield HH titration behavior [13],... 

Coupling between adjacent single protons, (a) First-order coupling, AX. (b) Second order coupling, AB -> A2. 

The correlation between the X-ray crystallographic data of the W—CN bond lengths and the first-order coupling constants between the 183W and 13C in the equatorial cyano ligands, as predicted by the Fermi-contact term (51), is fairly good (see Table III). This illustrates the increase in cis W—CN bond length induced by increased donor... 

Proton Chemical Shifts and First-Order Coupling-Constants for Selected KDO Derivatives0 (Ref. 81)... 

Compound number Chemical shift (6, p.p.m.) First-order coupling-constants (Hz) ... 

Ep shifts with the scan rate v at slow scan rates (where the chemical reaction is dominating), 9Ep/9 log v = 30/v mV for a first-order coupled chemical reaction... 

These two ordinary differential equations are a nonlinear, first-order coupled system, with the axial coordinate z as the independent variable. The dependent variables are U and p. 

The delay in the tubuloglomerular feedback is represented by means of three first-order coupled differential equations ... 

With this information in hand, search the proton NMR spectrum for confirmation and further leads. If the spectrum allows, determine the total proton count and ratios of groups of chemical shift-equivalent protons from the integration. Look for first order coupling patterns and for characteristic chemical shifts. Look at the 13C/DEPT spectra determine the carbon and proton counts and the numbers of CH3, CH2, CH, and C groups. A discrepancy between the proton integration and the... 

Figure 5.1 The effect of quadrupole interactions on an / = 3/2 nucleus in a magnetic field. The Zeeman interaction splits the levels by an equal amount, cot, (the Larmor frequency in frequency units). The central +1 /2 to -1 /2 transition is unaffected by first order coupling co j however, second order coupling, co , affects all transitions.

---