Ab Initio
Multiple Spawning Dynamics
Todd J. Martínez
Department of Chemistry & The Beckman Institute
University of Illinois at UrbanaChampaign
Ab Initio
Molecular Dynamics Terminology
Classical
No
Any
DFT
Ab initio
BOMD
BornOppenheimer
Molecular Dynamics
Classical
No
Any
DFT
Ab initio
Semiempirical
Direct Dynamics
Classical
Yes
Gaussian
DFT or SCF
ADMP
AtomCentered Density
Matrix Propagation
Classical
Yes
Plane Wave
DFT
CPMD
CarParrinello Molecular
Dynamics
Dynamics
Extended
Lagrangian?
Electronic
Basis
Electronic
Structure
Electronic Basis Sets
z
Plane waves 
–
Natural for periodic systems
–
HellmanFeynman Forces are exact
–
Very inefficient for nonperiodic systems (large empty spaces between periodic
replicas; in almost all cases, this empty space is filled with basis functions)
–
Obvious, welldefined convergence hierarchy
z
Gaussian –
–
Periodicity is more difficult to incorporate (but not impossible, e.g.
Crystal
)
–
Generally atomcentered (“floating” Gaussians also possible)
z
Electrons like to be near nuclei!
–
Pulay terms in forces for atomcentered Gaussians
–
Convergence hierarchy more subtle, but now wellunderstood (Dunning)
2
r
e
α
−
ikr
e
…
…
Empty space
“Pulay” Terms
()
;;
ˆˆ
ˆ
ˆ
elec
el
elec
elec
elec
elec
elec
ele
elec
el
ec
elec
r
ec
elec
r
r
c
r
H
rR
E
rR H
r
Hr
R
r
R
R
R
R
R
R
H
R
ψψ
=
∂∂
+
∂
∂
=
∂
∂
∂
+
∂
∂
∂
“HellmannFeynman Force”
“Pulay Force”
Pulay force
apparently
requires derivatives of electronic wavefunctions!
Actually, often it does
not
, but it
is
always more expensive than HF Force
Extended Lagrangian Technique
z
What is it?
–
Electronic degrees of freedom are
propagated
under a new Lagrangian, instead of
using the variational principle to determine them at each new geometry
z
Benefits
–
Wavefunction does not need to be converged at each time step
z
“1” iteration vs. typical 1015 iterations (apparently)
z
But
, good BOMD codes require < 5 iter b/c geometry change in one time step is small
z
Disadvantages
–
Need to ensure that the electronic coefficients are always “cold” and nuclei are
always “hot”
z
Energy transfer between ions and “fictitious” degrees of freedom is
unphysical
–
Time step needs to be smaller than in BOMD – fictitious degrees of freedom are
highfrequency
relative to nuclei
z
Bottom line (according to TJM)
–
EL schemes have ½ time step to save 5 iterations/time step.
Works out to a 2.5x
speed advantage in favor of EL
–
But
need to be careful to maintain adiabatic separation of nuclei and electrons.
–
Both are reasonable and choice depends on taste
EL expands dynamic range of frequencies to reduce SCF iterations
Electronic Excited States
CC
H
Ph
H
Ph
(CH3)2C
C(CH3)2
h
ν
Ph
Ph
CH3
CH3
CH3
CH3
+
N
N
N
N
Mg
O
R
CO2CH3
N
Opsin
H
Chemical Synthesis
Energy Conversion
Vision
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View Full DocumentLightDriven Molecular Devices
F
h
ν
F
Switch electron transport on and off
Light
→
Mechanical Work
Other Applications…
Optical Memory
Molecular Logic
Local control of pH –
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 Summer '06
 DuaneJohnson
 Electron, Mole, Quantum Chemistry, Computational chemistry, FMS, basis functions, conical intersection

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