Sentence examples for matrix elements between from inspiring English sources

The complex approach to the investigation of optical properties includes some steps: neglect all matrix elements between bonding and anti-bonding states; reduce Hamiltonian matrix to two matrixes, one of which is constructed on valence band conditions, and another on conductive band conditions; use Wannier functions for zeroing of matrix elements between bonding and anti-bonding states in matrix.

We present an efficient method for the calculation of matrix elements between two plane waves interacting with a molecular Coulombic field.

The imaginary part can be obtained from the momentum matrix elements between the unoccupied and occupied wave functions within the selection rules, and the real part can be calculated from the imaginary part by Kramers-Kronig correlations.

As the result, one can obtain the diagonal matrix elements, which correspond to Wannier energy levels, as well as matrix elements between the bonding states, responsible for splitting of these levels in bands.

Due to symmetry property of the atomic orbitals, only a few angular momentum matrix elements between the d orbitals are nonzero: 〈xz|L z |yz〉, 〈x 2−y 2|L z |xy〉, 〈z 2|L x |yz〉, 〈xy|L x |xz〉, and 〈x 2−y 2|L x |yz〉 (bra and ket can be exchanged).

However, the decrease of ligand electronegativity results in a slight decrease in molecular rigidity and the SOC matrix elements between the ground state and the lowest triplet excited state increase, the energy barriers in photodeactivation pathway decrease, which eventually leads to the increase of nonradiative decay rate constant.

Here, V spσ represents the transfer matrix element between the outermost p orbital and the lowest excited of s state.

(c) The results appear for two values of the applied electric field with P = 0 and α0 = 0. Figure 5 The transition dipole matrix element between the ground and first-excited exciton states in a cylindrical QD.

Here, ( {varepsilon}_i^{mu} ) denotes the on-site energy of i-site with μ orbital (μ = s, p) and ( {t}_{ji}^{mu nu} ) denotes the transfer matrix element between the μ orbital in i-site and the ν orbital in j-site.

The covalency term in the interaction potential is thus expressed as [16, 17]: f_{text{cov}} (r) = frac{{4e^{2} V_{spsigma }^{2} }}{{r_{0} E_{text{g}}^{3} }} (12)Here, V spσ represents the transfer matrix element between the outermost p orbital and the lowest excited of s state.

Especially, the high quantum yield of 3b compared with 3a is explained based on the detailed analysis of the triplet energy (ET1), transition dipole moment (μS1) upon the S0 → S1, SOC matrix element between the Tm and Sn states, ΔES1−Tm, 3MLCT% in the phosphorescent spectra, energy difference between 3MLCT and electronic configurations of the triplet metal-centered (3MC) d d excited states.