Full-dimensional quantum molecular dynamics calculations of the rovibrationally mediated X
1A′ → 2
1A′′ transition of nitrous oxide

Daud, Mohammad Noh

doi:10.1002/qua.25065

Cited by 5 publications

(9 citation statements)

References 49 publications

(157 reference statements)

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“…Due to the fact that the kinetic energy operators in Equation (1) are diagonal in momentum space, I can transform

ψ

to its momentum representation via the fast Fourier transform technique and transform back to the coordinate representation [52–54] to obtain the explicit form of Equation () as

\begin{matrix} alignleft \\ align-1 i \frac{\partial ψ (z_{1}, z_{2}, R, ϑ, t)}{\partial t} & align-2 = \frac{1}{2 m_{N} π} \int_{- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} \{\int_{0}^{\infty} e^{- i k_{R} R} ψ (z_{1}, z_{2}, R, ϑ, t) d R\} d k_{R} \\ align-1 & align-2 + \frac{1}{4 π} \sum_{i = 1}^{2} \int_{- \infty}^{\infty} k_{z_{i}}^{2} e^{i k_{z_{i}} z_{i}} \{\int_{0}^{\infty} e^{- i k_{z_{i}} z_{i}} ψ (z_{1}, z_{2}, R, ϑ, t) d z_{i}\} d k_{z_{i}} \\ align-1 & align-2 - {\sum_{i = 1}^{2} ( \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

“…Some portions of the wave packet eventually reach the boundary of the numerical grid. I employ a complex absorbing potential near the boundaries that can absorb the outgoing wave packets, avoiding reflection back into the inner part of the grid [40,52–54]:

\begin{align} V_{abs} false(z_{1}, z_{2}, R false) = ({, \begin{matrix} array 0.0 & array; |z_{i}| < z_{abs}, R < R_{abs} \\ array - i \{γ \sum_{i = 1}^{2} {(|z_{i}| - z_{abs})}^{\bar{γ}} + i β {(R - R_{abs})}^{\bar{β}}\} & array; z_{abs} \leq |z_{i}| \leq z_{\max}, R_{abs} \leq R \leq R_{\max} \end{matrix}) \end{align}

With this scheme, the absorber is turned on at

R_{abs} = 40

a.u. and

z_{abs} = 246

a.u., while I optimize the dimensionless parameters

γ = 0.001

\bar{γ} = 2

β = 0.01

and

\bar{β} = 2 ...

…”

Section: Theorymentioning

confidence: 99%

“…Thus I can transform

ψ_{v}^{i} (i = g, u)

to its momentum representation via the fast Fourier transform technique and transform back to the coordinate representation [52–54] to obtain

\begin{align} i \frac{\partial}{\partial t} ψ_{v}^{g} false(R, t false) & = \frac{1}{2 m_{N} π} \int_{prefix- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} ({}, \int_{0}^{\infty} e^{prefix- i k_{R} R} ψ_{v}^{g} false(R, t false) d R) d k_{R} \\ + ({}, V_{-}^{a} false(z_{1} : R false) + ([], V_{+}^{a} false(z_{1} : R false) prefix- V_{-}^{a} false(z_{1} : R false))) ψ_{v}^{g} false(R, t false) \sin^{2} θ + V_{g u} ψ_{v}^{u} false(R, t false) \end{align}

\begin{align} i \frac{\partial}{\partial t} ψ_{v}^{u} false(R, t false) & = \frac{1}{2 m_{N} π} \int_{prefix- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} ({}, \int_{0}^{\infty} e^{prefix- i k_{R} R} ψ_{v}^{u} false(R, t false) d R) d k_{R} \\ + ({}, V_{+}^{a} false(z_{1} :<...) \end{align}

…”

Section: Theorymentioning

confidence: 99%

“…where t tot is the pulse duration, I ¼ 4 Â 10 14 W Á cm À2 is the applied laser intensity and I a ¼ 3:5 Â 10 16 W Á cm À2 . With the chosen wavelength λ ¼ 800 nm, Figure 1 shows the six optical cycles laser pulse at fixed of ϑ ¼ 0 ∘ and ϑ ¼ 90 Due to the fact that the kinetic energy operators in Equation ( 1) are diagonal in momentum space, I can transform ψ to its momentum representation via the fast Fourier transform technique and transform back to the coordinate representation [52][53][54] to obtain the explicit form of Equation (1) as…”

mentioning

confidence: 99%

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Strong‐field coherent control of the proton momentum distribution arising from the n‐photon (n=1,2,3) field‐dressed adiabatic potentials of H2+

Daud

2023

Int J of Quantum Chemistry

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A systematic directionality coherent control of total proton momentum distributions in the dissociative‐ionization of H subjected to a strong field of six‐cycle laser pulses in a full range of carrier‐envelope phase is studied by solving a non‐Born‐Oppenheimer time‐dependent Schrödinger equation numerically. The trend of distributions involves insightful investigation into the spatial‐temporal overlap between nuclear wave packets evolving on the coupled field‐dressed electronic potentials of H associated with the ‐photon potential crossings. This leads to new quantum images for the nonlinear nonperturbative interaction of H with a strong field. It turns out that the symmetry of the ‐dependent momentum distribution begins to break after undergoing interaction with one‐photon field‐dressed potentials. At this point, the most probable proton momentum distribution tends to move in a forward direction indicating also that the three‐photon field‐dressed potentials strongly govern the dissociative‐ionization pathway.

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“…Due to the fact that the kinetic energy operators in Equation (1) are diagonal in momentum space, I can transform

ψ

to its momentum representation via the fast Fourier transform technique and transform back to the coordinate representation [52–54] to obtain the explicit form of Equation () as

\begin{matrix} alignleft \\ align-1 i \frac{\partial ψ (z_{1}, z_{2}, R, ϑ, t)}{\partial t} & align-2 = \frac{1}{2 m_{N} π} \int_{- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} \{\int_{0}^{\infty} e^{- i k_{R} R} ψ (z_{1}, z_{2}, R, ϑ, t) d R\} d k_{R} \\ align-1 & align-2 + \frac{1}{4 π} \sum_{i = 1}^{2} \int_{- \infty}^{\infty} k_{z_{i}}^{2} e^{i k_{z_{i}} z_{i}} \{\int_{0}^{\infty} e^{- i k_{z_{i}} z_{i}} ψ (z_{1}, z_{2}, R, ϑ, t) d z_{i}\} d k_{z_{i}} \\ align-1 & align-2 - {\sum_{i = 1}^{2} ( \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

\begin{align} V_{abs} false(z_{1}, z_{2}, R false) = ({, \begin{matrix} array 0.0 & array; |z_{i}| < z_{abs}, R < R_{abs} \\ array - i \{γ \sum_{i = 1}^{2} {(|z_{i}| - z_{abs})}^{\bar{γ}} + i β {(R - R_{abs})}^{\bar{β}}\} & array; z_{abs} \leq |z_{i}| \leq z_{\max}, R_{abs} \leq R \leq R_{\max} \end{matrix}) \end{align}

With this scheme, the absorber is turned on at

R_{abs} = 40

a.u. and

z_{abs} = 246

a.u., while I optimize the dimensionless parameters

γ = 0.001

\bar{γ} = 2

β = 0.01

and

\bar{β} = 2 ...

…”

Section: Theorymentioning

confidence: 99%

“…Thus I can transform

ψ_{v}^{i} (i = g, u)

to its momentum representation via the fast Fourier transform technique and transform back to the coordinate representation [52–54] to obtain

\begin{align} i \frac{\partial}{\partial t} ψ_{v}^{g} false(R, t false) & = \frac{1}{2 m_{N} π} \int_{prefix- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} ({}, \int_{0}^{\infty} e^{prefix- i k_{R} R} ψ_{v}^{g} false(R, t false) d R) d k_{R} \\ + ({}, V_{-}^{a} false(z_{1} : R false) + ([], V_{+}^{a} false(z_{1} : R false) prefix- V_{-}^{a} false(z_{1} : R false))) ψ_{v}^{g} false(R, t false) \sin^{2} θ + V_{g u} ψ_{v}^{u} false(R, t false) \end{align}

\begin{align} i \frac{\partial}{\partial t} ψ_{v}^{u} false(R, t false) & = \frac{1}{2 m_{N} π} \int_{prefix- \infty}^{\infty} k_{R}^{2} e^{i k_{R} R} ({}, \int_{0}^{\infty} e^{prefix- i k_{R} R} ψ_{v}^{u} false(R, t false) d R) d k_{R} \\ + ({}, V_{+}^{a} false(z_{1} :<...) \end{align}

…”

Section: Theorymentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Strong‐field coherent control of the proton momentum distribution arising from the n‐photon (n=1,2,3) field‐dressed adiabatic potentials of H2+

Daud

2023

Int J of Quantum Chemistry

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“…Therefore, the promotion must subject to upon an initial electronic‐nuclear wave packet consisting of

g

symmetry‐type electronic wave function:

ψ ((),,,,, z_{1}, z_{2}, R, ϑ, t = 0) = μ_{z} ((),, ϑ, t) ψ_{i} ((),,, z_{1}, z_{2}, R),

where

μ_{z} ((),, ϑ, t) = (〈〉,,,,, ψ ((),,,,, z_{1}, z_{2}, R, ϑ, t) (||, (z_{1} + z_{2})) ψ true(z_{1}, z_{2}, R, ϑ, t true)),

is the z ‐component of the laser‐induced transition dipole moment connecting the electronic states, and the evolution of

ψ

as the electronic‐nuclear ground state wave function for H 2 starting from t = 0 propagated in time using Equations (). Generally,

ψ_{i} ((),,, z_{1}, z_{2}, R)

can be written as a product of electronic and nuclear Born‐Oppenheimer wave functions,

ψ_{i} ((),,, z_{1}, z_{2}, R) = σ_{g} ((),, z_{1}, z_{2} : R) ψ_{g, v} ((), R : E_{i}),

where

σ_{g}

is the electronic wave function parametrically depending on all nuclear degrees of freedom

R

and

ψ_{g, v}

is the eigenfunction (represents the bound‐state nuclear wave function) of the time‐independent Schrödinger equation [39]

\begin{matrix} lefttrue \\ \{- \frac{1}{m_{N}} \frac{\partial^{2}}{\partial R^{2}} + V (z_{<...>})\} \end{matrix}

…”

Section: Theorymentioning

confidence: 99%

Controlling quantum wave packet of electronic motion on field‐dressed Coulomb potential of by carrier‐envelope phase‐dependent strong field laser pulses

Daud

2021

Int J of Quantum Chemistry

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Solving numerically a non‐Born‐Oppenheimer time‐dependent Schrödinger equation to study the dynamics of H2 subjected to strong field six‐cycle laser pulses (I=4×1014 W/cm2, λ=800 nm) leads to the newly ultrafast electron imaging in the dissociative‐ionization of H2+. This includes the electron distribution in H2+ oscillates symmetrically with laser cycle with ϑ+π periodicity where the distribution concentrates between two protons for about 8 fs, being trapped in a Coulomb potential well. Nonetheless, the most important finding reveals that the electron symmetrical distribution begins to break up in the field‐free region after 24 fs when the H2+ internuclear distance stretches larger than 9 a.u. It is a result of the distortion of Coulomb potential where the ejected electron preferentially localizes in one of the double‐well potential separated by the inner Coulomb potential barrier, leading to the new images of charge resonance enhanced ionization. Controlling laser carrier‐envelope phase ϑ enables one to quantify such phenomena with the highest total asymmetries Aetot of 0.75 and −0.75 occur at 10° and 190°, respectively, associated with the electron preferential directionality being ionized to the right and the left paths along the H2+ molecular axis.

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Ultrafast quantum imaging in the dissociation of H2+ via the induced conical intersection of two lowest adiabatic states by strong field laser pulses

Daud

2021

Chemical Physics

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Full-dimensional quantum molecular dynamics calculations of the rovibrationally mediated X 1A′ → 2 1A′′ transition of nitrous oxide

Cited by 5 publications

References 49 publications

Strong‐field coherent control of the proton momentum distribution arising from the n‐photon (n=1,2,3) field‐dressed adiabatic potentials of H2+

Strong‐field coherent control of the proton momentum distribution arising from the n‐photon (n=1,2,3) field‐dressed adiabatic potentials of H2+

Controlling quantum wave packet of electronic motion on field‐dressed Coulomb potential of by carrier‐envelope phase‐dependent strong field laser pulses

Ultrafast quantum imaging in the dissociation of H2+ via the induced conical intersection of two lowest adiabatic states by strong field laser pulses

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