ESEEM simulation Sample Clauses

ESEEM simulation. Numerical simulations of the ESEEM simulations were performed by using the Matlab-based code in the OPTESIM software package, which we have recently presented and described in detail.126 The stationary-state spin Hamiltonian for treatment of the interaction of the electron spin (S=1/2) on Cu(II) with the remote 14N nuclear spin (I=1) is formulated with a shf coupling term, a nuclear Zeeman term, and a nqi term, as follows:127 where N,  H  hS  A  I  g N  N B0  I  I  Q  I ' S , and I are the nuclear magneton, electron spin operator, and nuclear spin  [4.3.3.1] operator, respectively, g N is the nuclear g-value, A is the shf coupling tensor, and Q is the nuclear quadrupole interaction tensor.128 The I and I’ indicate that the eigenfunctions of A and Q are, in general, different. The superhyperfine tensor has the principal components, A  A A A , and is composed of an isotropic part, A  1  A , and a dipolar part, AP – Aiso. The nqi tensor, Q, is defined by the iso ii nuclear quadrupole coupling constant, e2qQ/h, and the efg asymmetry parameter, η.129 p xx yy zz In its PAS, the traceless nqi tensor Q  Q Q Q  is related to e2qQ/h and η by the following expressions: Qzz  e2qQ 2I 2I  1h xx Q  Q    yy Qzz where Qzz  Qyy  Qxx . In OPTESIM, the orientation between the nuclear quadrupole interaction tensor principal axis system and the hyperfine tensor principal Q Q axis system is defined by the Xxxxx xxxxxx,    . Xx systems with more than one coupled nucleus (N>1), the orientation of the superhyperfine principal axis system of each nucleus relative to an arbitrary reference frame is defined by the Euler angles,  A   . For the two remote N couplings in the Cu(II)-bis-imidazole A A complexes studied here,  A  A  A are chosen to define the mutual orientation of the two superhyperfine principal axis system. The coupled electron – single 14N system is therefore parameterized by using the following eight adjustable parameters: Axx, Ayy, Azz, X, X, X, x0xX/x, η. In the Cu(II)-bis-imidazole complexes, the eight parameters are assumed to be common among the two imidazole 14N. The bis-imidazole complexes have A, A, and A, as additional adjustable parameters. The method of calculation of the simultaneous confidence region for each adjustable parameters, at a specific confidence level (here, 99%), has been described in detail.126 The ESEEM calculation in OPTESIM incorporates the full density matrix diagonalization from the Xxxx ...