8/6/2023 0 Comments Hf dipole moment![]() δ Θ X + δ Θ H is always negative while Θ HX proto is positive, so one can approximate the molecular quadrupole moment to within 10% as Θ ( HX ) > Θ HX proto + 2 μ H R + q H R 2. LC-BLYP functional can be used to estimate excited state electric properties. LC-functionals are in good agreement with elaborate Coupled cluster calculations. LC-functionals yield more reliable results than the standard hybrid functionals. The maximum in the QMF and its slope at equilibrium are determined essentially by 2 μ H R + q H R 2, which is known once the DMF is known. Excited state dipoles and polarizability were calculated by TDDFT and finite-field. The quadrupole moment function (QMF) (with the halogen as origin) is given by Θ ( HX ) = Θ HX proto + δ Θ X + δ Θ H + 2 μ H R + q H R 2, where Θ HX proto is the quadrupole moment of the separated atoms (the halogen in this instance) and δ Θ X + δ Θ H the change in the in situ quadrupole moments of the halogen and hydrogen atoms. μ Cl, μ Br, and μ I, on the other hand, are increasingly more negative at the maximum of q H R + μ H and have a profound effect on the width of the maximum of the resulting DMF, successively broadening it and completely eliminating it at HI. In HF, μ F is slightly positive at the maximum in q H R + μ H and has little effect on the resultant maximum in the dipole moment function (DMF). Greater differences in electronegativity will consequently lead to larger dipole moments. ![]() We find that q H R + μ H is always positive and has a maximum at bond lengths larger than the equilibrium. A dipole moment is a result of unequal electron distribution, which occurs due to differences in electronegativity between chemically-bonded atoms (since electrons tend to move towards more electronegative atoms). The dipole moment is the sum of the functions q H R + μ H and μ X with q H being the charge on the hydrogen atom, R the internuclear separation, μ H and μ X the atomic dipoles on the hydrogen and halogen atoms. These functions are analyzed in terms of local moments constructed using the Hirshfeld method. The dipole and quadrupole moment functions of the hydrogen halides are calculated using a large polarized basis and correlated wavefunctions and compared to experiment and previous calculations.
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