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See EPAPS Document No. E-JCPSA6-130-001911 for Table SI elaborating energetic and structural information for ground-state and excited-state calculations; Table SII containing explicit harmonic frequencies for the TrOD isotopolog calculated by the CIS, TDDFT (B3LYP), and EOM-CCSD methods using the aug-cc-pVDZ basis set; Tables SIII and SIV enumerating the contributions of ground-state and excited-state normal modes to vibrationally averaged inertial defects; and Figure S1 illustrating the normal coordinate vectors for each of the 39 vibrational modes emerging from EOM-CCSD/aug-cc-pVDZ force-field analyses of the PL (Cs) equilibrium framework for à B1 2 TrOH. For more information on EPAPS, see.
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See EPAPS Document No. E-JCPSA6-130-001911 for Table SI elaborating energetic and structural information for ground-state and excited-state calculations; Table SII containing explicit harmonic frequencies for the TrOD isotopolog calculated by the CIS, TDDFT (B3LYP), and EOM-CCSD methods using the aug-cc-pVDZ basis set; Tables SIII and SIV enumerating the contributions of ground-state and excited-state normal modes to vibrationally averaged inertial defects; and Figure S1 illustrating the normal coordinate vectors for each of the 39 vibrational modes emerging from EOM-CCSD/aug-cc-pVDZ force-field analyses of the PL (Cs) equilibrium framework for à B1 2 TrOH. For more information on EPAPS, see http://www.aip.org/pubservs/epaps.html.
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Specifically, correlated modes i à and i X̃, where i=1,2,39, appear in the same position in the two tables irrespective of any monotonic excited-state numbering.
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Specifically, correlated modes i à and i X̃, where i=1,2,39, appear in the same position in the two tables irrespective of any monotonic excited-state numbering.
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For a normal coordinate that has not been mass weighted, k, the corresponding reduced mass can be computed in the standard manner to find μk = ∥ m1/2 lk ∥ 2 / ∥ lk ∥ 2 = ∥ m1/2 (rk - r0) ∥ 2 / ∥ rk - r0 ∥ 2, where rk and r0 denote the collective sets of displaced and equilibrium Cartesian coordinates, respectively, with the numerator being unity by normalization for a unit (mass-weighted) ste(Qk =1). In the case of 39, the resulting μ 39 X̃ =5.856 amu and μ 39 Ã =6.190 amu parameters are valid for the harmonic (HO) and the natural anharmonic (AO) potentials since both use the canonical definition for the attendant displacement coordinate. Applying the same procedure to the partially relaxed anharmonic (PO) form (rk = r 39 PO) yields average values of μ 39 X̃ =6.041 amu and μ 39 Ã =6.197 amu.
-
For a normal coordinate that has not been mass weighted, k, the corresponding reduced mass can be computed in the standard manner to find μk = ∥ m1/2 lk ∥ 2 / ∥ lk ∥ 2 = ∥ m1/2 (rk-r0) ∥ 2 / ∥ rk-r0 ∥ 2, where rk and r0 denote the collective sets of displaced and equilibrium Cartesian coordinates, respectively, with the numerator being unity by normalization for a unit (mass-weighted) step (Qk =1). In the case of 39, the resulting μ 39 X̃ =5.856 amu and μ 39 Ã =6.190 amu parameters are valid for the harmonic (HO) and the natural anharmonic (AO) potentials since both use the canonical definition for the attendant displacement coordinate. Applying the same procedure to the partially relaxed anharmonic (PO) form (rk = r 39 PO) yields average values of μ 39 X̃ =6.041 amu and μ 39 Ã =6.197 amu. These alternate reduced masses have negligible effect on the fundamental energy separations and vibrationally averaged inertial defects calculated for the PO model.
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66
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65249158727
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Symmetry constraints permit only even quanta of 39 to be observed in the à - X̃ transition.
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Symmetry constraints permit only even quanta of 39 to be observed in the Ã-X̃ transition.
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65249191088
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For a mass-weighted displacement Q along a given out-of-plane (a″) normal mode in a molecule supporting a planar (Cs) minimum-energy configuration, the Eckart-Sayvetz conditions will serve to align the equilibrium and instantaneous inertial axes. Since the inertial tensor of the displaced frame can be shown to differ from that of the equilibrium frame only for the two diagonal elements that reside in the molecular plane (i.e., Ia → Ia + Q2, Ib → Ib + Q2, and Ic → Ic with all off-diagonal elements equal to zero), the corresponding inertial-defect function may be evaluated readily as ΔI (Q) =-2 Q2.
-
For a mass-weighted displacement Q along a given out-of-plane (a″) normal mode in a molecule supporting a planar (Cs) minimum-energy configuration, the Eckart-Sayvetz conditions will serve to align the equilibrium and instantaneous inertial axes. Since the inertial tensor of the displaced frame can be shown to differ from that of the equilibrium frame only for the two diagonal elements that reside in the molecular plane (i.e., Ia → Ia + Q2, Ib → Ib + Q2, and Ic → Ic with all off-diagonal elements equal to zero), the corresponding inertial-defect function may be evaluated readily as ΔI (Q) =-2 Q2.
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