Electric-field-induced adiabaticity in the rovibrational motion of heteronuclear diatomic molecules

We investigate the rovibrational dynamics of heteronuclear diatomic molecules exposed to a strong external static and homogeneous electric field. We encounter in the presence of the field the effect of induced adiabatic coupling among the vibrational and hybridized rotational motions. Exact results are compared to the predictions of the adiabatic rotor approach as well as to the previously established effective rotor approximation. A detailed analysis of the impact of the electric field is performed: the hybridized and oriented rotational motion, the mixing of angular momenta, and the squeezing of the vibrational motion are observed. It is demonstrated that these effects can well be accounted for by the adiabatic rotor approximation.

Figure 1

Field-free vibrational energy spacings (엯) for the Morse potentials with $R_e=2.2\mathrm{a.u.}$ and $R_e=6.0\mathrm{a.u.}$ as a function of the vibrational quantum number $\nu$. Field-free rotational energy spacings for the Morse with $R_e=2.2\mathrm{a.u.}(+)$ and $R_e=6.0\mathrm{a.u.}(\star )$ as a function of the vibrational quantum number $\nu$.

Figure 2

The electric dipole moment functions used in our computations, centered $D_C$, shifted $D_S$, and wider $D_W$ as a function of $R-R_e$.

Figure 3

(Color online) (a) The expectation values $⟨\cos \theta ⟩$, (b) the relative error $\Delta {⟨\cos \theta ⟩}_{\nu }^{\mathcal{E}}$ of the effective rotor approximation, (c) the relative error $\Delta {⟨\cos \theta ⟩}_{\nu }^{\mathcal{A}}$ of the adiabatic rotor approximation as a function of the vibrational label $0⩽\nu ⩽20$ for states emerging from $J=0$ for $F=0$ for the Morse potential with $R_e=6.0\mathrm{a.u.}$ and the three EDMFs $D_C$ (◇), $D_S(+)$, and $D_W$ (◻).

Figure 4

(Color online) (a) The expectation values $⟨{\mathbf{J}}^2⟩$, (b) the relative error $\Delta {⟨{\mathbf{J}}^2⟩}_{\nu }^{\mathcal{E}}$ of the effective rotor approximation, (c) the relative error $\Delta {⟨{\mathbf{J}}^2⟩}_{\nu }^{\mathcal{A}}$ of the adiabatic rotor approximation as a function of the vibrational label $0⩽\nu ⩽20$ for states emerging from $J=0$ for $F=0$ for the Morse potential with $R_e=6.0\mathrm{a.u.}$ and the three EDMFs $D_C$ (◇), $D_S(+)$, and $D_W$ (◻).

Figure 5

(Color online) (a) The expectation values $⟨R⟩$, (b) the relative error $\Delta {⟨R⟩}_{\nu }^{\mathcal{E}}$ of the effective rotor approximation, (c) the relative error $\Delta {⟨R⟩}_{\nu }^{\mathcal{A}}$ of the adiabatic rotor approximation as a function of the vibrational label $0⩽\nu ⩽20$ for states emerging from $J=0$ for $F=0$ for the Morse potential with $R_e=6.0\mathrm{a.u.}$ and the three EDMFs $D_C$ (◇), $D_S(+)$, and $D_W$ (◻). For completeness the field-free values of $⟨R⟩(\times )$ have also been included.

Figure 6

(Color online) Same as in Fig. 3 but for $R_e=2.2\mathrm{a.u.}$

Figure 7

(Color online) Same as in Fig. 4 but for $R_e=2.2\mathrm{a.u.}$

Figure 8

(Color online) Same as in Fig. 5 but for $R_e=2.2\mathrm{a.u.}$

Figure 9

(Color online) Probability density of the rovibrational ground state of the Morse potential with $R_e=6.0\mathrm{a.u.}$ and the centered EDMF for the field strength $F={10}^{-3}\mathrm{a.u.}$

Figure 10

(Color online) Probability density of the rovibrational ground state of the Morse potential with $R_e=2.20\mathrm{a.u.}$ and $D_W$ for the field strength $F={10}^{-3}\mathrm{a.u.}$

Figure 11

(Color online) Probability density of the state $\nu =5$ emerging from the field-free $J=0$ state of the Morse potential with $R_e=2.20\mathrm{a.u.}$ and $D_S$ for the field strength $F={10}^{-3}\mathrm{a.u.}$