Upload
others
View
10
Download
0
Embed Size (px)
Citation preview
1-site fragment
2-site fragment
Theoretical Methods for Dynamics of Correlated Electrons, Ions and Photons
Time-dependent density functional theory (TDDFT) is the most widely used method to get electronic excitations and dynamics in molecules and solids.
*Email [email protected] to find out more!
e.g. Hubbard tetramer: two sites with fixed interaction and two sites with variable
𝑈′ = 0.1 𝑈
Systems containing strong correlation require us to go beyond usual density-functional methods. We are developing a new, practical, first-principles quantum electronic embedding based on exact factorization (EF) in Fock Space:
e.g. 100-site uniform Hubbard ring, EVEF (dash-dot), exact (solid)
Use mean-field method Ψ extract Φn and embedding h solve for fragment χ with high-level method accurate energy E
→ → →h𝜒 = 𝐸𝜒 →
Site-occupations for chosen fragment, e.g. those with strongly-correlated orbitals
Embedding Hamiltonian:
N. M. Hoffmann, H.Appel, A.Rubio, N. T. Maitra, Eur. Phys. J. B. 91, 180 (2018). L. Lacombe, N. M. Hoffmann, N. T. Maitra, Phys. Rev. Lett. 123, 083201 (2019).
https://sasn.rutgers.edu/about-us/faculty-staff/neepa-maitra
For factorize𝐻Ψ = 𝐸Ψ,
L. Lacombe and N. T. Maitra, arXiv 1909.07416 (2019)
àTDSE for the photons à corrections to the quadratic form due to
matter-photon coupling
àTDSE for the nuclei àExact potential driving the nuclei coupled
to electrons and photons
•EVEF captures full range of weak to strong correlation well.
•EF gives cavity-modified time-dependent potential energy surfaces for proton-coupled electron transfer that directly indicate suppression:
cavity-freeIn-cavity λ =0.005In-cavity λ =0.001
Ehrenfest trajectories for
photons’ displacement field coordinates work
well.
• Build improved approximations for the exchange-correlation potential ( ), especially for cases where the usual approximations fail.υXC
N. T. Maitra, J. Chem. Phys. 144, 220901 (2016); J. Phys. Condens. Matt. 29, 423001 (2017). Y. Suzuki, L. Lacombe, K. Watanabe, and N. T. Maitra, Phys. Rev. Lett. 119, 263401 (2017). L. Lacombe, N. T. Maitra, J. Chem. Theory and Comput. 15,1672 (2019).
In particular:
Our density-matrix coupled approach has memory, and satisfies exact
conditions important for time-dynamics:
•The Exact Factorization (EF) approach allows to understand how quantum subsystems’ dynamics influence each other, and to develop mixed quantum-classical methods.
A. Abedi, N. T. Maitra, EKU Gross, Phys. Rev. Lett. 105, 123002 (2010); J. Chem. Phys. 137, (2012) G. H. Gossel, F. Agostini, N. T. Maitra, J. Chem. Theory Comput. 14, 4513 (2018). G. H. Gossel, L. Lacombe, N. T. Maitra, J. Chem. Phys. 150, 154112 (2019).
✦The exact equations for χ and ΦR contain potentials that exactly capture the electron-nuclear correlation. They give rise to rigorous mixed quantum-classical methods, including surface-hopping approaches with first-principles decoherence corrections.
Electron Dynamics via TDDFT
Our work:
i∂tϕi(r, t) = ( − ∇2/2 + υs(r, t))ϕi(r, t)
υs[n; Φ0](rt) = υext(rt) + ∫ d3r′ n(r′ t)
|r − r′ |+ υXC[n; Ψ0, Φ0](rt)
Neepa T. Maitra*, Lionel Lacombe, Patricia Vindel Zandbergen, Norah Hoffmann, Davood Dar
Memory is missing from the usual approximations
Inaccurate dynamics (e.g.: charge-transfer, resonant driving, scattering…)
υXC
Dependence of on the density at earlier
times and the initial states.
υXCn(r, t)
i∂tϕj(r, t) = ( − ∇2 /2 + υext(r, t) + υH(r, t) + υXC(r, t))ϕj(r, t)
∇ ⋅ (n∇υxc) = ∇ ⋅ [14
(∇′ − ∇)(∇2 − ∇′ 2)(ρ1(r′ , r, t) − (ρ1,s(r′ , r, t))
υTc
|r′ =r + n(r, t)∫ nXC(r′ , r, t)∇w( |r′ − r | )d3r′ ]υW
xc
i∂ρ1
∂t= [ − ∇2 /2 + υext, ρ1](r, r′ , t) + ∫ d3r(w(r, r) − w(r′ , r))ρ2[ρ1, ρ1,s](r, r; r′ , r)
approximation herenxc
Prop
agatesid
e-by-side
Coupled Electron-Ion Dynamics via EF•Dynamics of molecules beyond the Born-Oppenheimer approximation is increasingly relevant in many areas, e.g. photo-induced processes, solar-cell design, biomolecular mechanism modeling.
Polaritonic Chemistry Electronic Embedding via EF (EVEF)
Ψ (n1, n2, . . nk,
n
nk+1, . . nM)
m
= χ(n)Φn(m)
hn;n′ ≡ ∑m′ ,m
Φ*n (m)Hn,m;n′ ,m′ Φn′ (m′ )
∑m
Φ*n (m)Φn(m) = 1Ψ(r, R, q, t) = χ(q, t)Φq(r, R, t) = χ(R, t)ΦR(r, q, t) = χ(r, t)Φr(q, R, t)
H = HBO + Veext(r, t) + Tn(R) + Vn
ext(R, t)
HBO = Te(r) + Wee(r) + Ven(r, R) + Wee(R)} HΨ(r, R, t) = i∂tΨ(r, R, t)
Ψ(r, R, t) = ΦR(r, t)χ(R, t) ∫ dr |ΦR(r, t) |2 = 1
EF
where
Molecule in a nanoscale cavity greatly enhances the light-matter coupling strength
Manipulate light and matter properties (recent experimental advances in cavity QED)
Hybrid light-matter states (polariton) Quantized nature of light becomes important
Exact factorization and trajectory methods to gain insight and model the new phenomena
Our work:ωα
λα:Coupling strength:Photonic frequency
Exact potential driving electron in laser driven molecular dissociation
✦ Coupled-trajectory approach based on the exact electron-nuclear correlation from the EF to describe
quantum (de)-coherence in large molecules
Dynamics of excited uracil cation: quantum (de)-coherence can be treated correctly at the same
computational cost as the original SH dynamics.