Transcript Electron impact calculation on biological molecules Andrea

Shape resonances localization and
analysis by means of the Single Center
Expansion e-molecule scattering theory
Andrea Grandi
and
N.Sanna and F.A.Gianturco
Caspur Supercomputing Center
and
University of Rome ”La Sapienza”
URLS node of the EPIC Network
[email protected]
Introduction
The talk will be organized as follows:

Introduction to the e-molecule scattering theory
based on the S.C.E. approach

SCELib(API)-VOLLOC code

Shape resonances analysis

Examples and possible applications

Conclusions and future perspectives
The SCE method
The Single Center Expansion method
Central field model :
•Factorization of the wave-function in radial and angular components
•Bound and continuum electronic states of atoms
•Extension to bound molecular systems
•Electron molecule dynamics, molecular dynamics, surface science,
biomodelling
The SCE method
The Single Center Expansion method
In the S.C.E. method we have a
representation of the physical world based on
a single point of reference so that any
quantity involved can be written as
The SCE method
In the SCE method the bound state wavefunction
of the target molecule is written as
The SCE method
Symmetry adapted generalized harmonics
Symmetry adapted real spherical harmonics
The SCE method
Where S stays for
The SCE method
The bound orbitals are computed in a multicentre
description using GTO basis functions of near-HFlimit quality - gk(a,rk)
Where N is the normalization coefficient
The SCE method
The radial coefficients are computed by integration
The quadrature is carried out using GaussLegendre abscissas and weights for  and GaussChebyshev abscissas and weights for , over a
dicrete variable radial grid
The SCE method
Once evaluated the radial coefficients each
bound one-electron M.O. is expanded as:
So the one-electron density for a closed shell may be
expressed as
The SCE method
and so we have the electron density as:
Where
then, from
all of the relevant
quantities are computed.
The SCE method
The Static Potential
And as usual:
The SCE method
Where :
The SCE method
The polarization potential:
Short range interaction
For r ≤ rc
Long range interaction
For r > rc
where rc is the cut-off radius
The SCE method
Short-range first model:
Free-Electron Gas Correlation Potential
FEG
corr
V
 r    hlmV hlm (r ) X
FEG
A1
hlm
( ,  )
 0.0311ln rs 0.0584 0.00133rs ln rs 0.0084 rs
  (1  7  r 1/ 2  4  r )
FEG
V hlm (r )   6 1 s 3 2 s

1/ 2
2
(1   r
 r )
1s
2s

with rs   3 4  (r ) and
=0.1423,1=1.0529,2=0.3334.
for rs 1.0
for r  1.0
s
The SCE method
Short-range second model:
Ab-Initio Density Functional (DFT) Correlation Potential
where Ec is the Correlation Energy
Short-range second model:
Ab-Initio Density Functional (DFT) Correlation Potential
The SCE method
We need to evaluate the first and second derivative of (r)
In a general case we have:
The SCE method
We need to evaluate the first and second derivative of (r)
In a general case we have:
The SCE method
Problems with the radial part:
Single center expansion of F,F’, and F” are time consuming
We performe a cubic spline of F to simplify the evaluation of
the first and second derivative
Problems with the angular part:
For large values of the angular momentum L it is possible to
reach the limit of the double precision floating point arithmetic
To overcame this problem it is possible to use a quadrupole
precision floating point arithmetic (64 bits computers)
The SCE method
Long-range :
The asymptotic polarization potential
The polarization model potential is then corrected
to take into account the long range behaviour
The SCE method
Long-range :
The asymptotic polarization potential
In the simple case of dipole-polarizability
av
0
0
0
av
0
0
0
av
The SCE method
Long-range :
The asymptotic polarization potential
Where
Usually in the case of a linear molecule one has
The SCE method
Long-range :
The asymptotic polarization potential
Where
The SCE method
Long-range :
The asymptotic polarization potential
In a more general case
Once evaluated the long range polarization potential
we generate a matching function to link the short
/ long range part of Vpol
The SCE method
The exchange potential: first model
The Free Electron Gas Exchange (FEGE) Potential
Two great approximations:
 Molecular electrons are treated as in a free electron
gas, with a charge density determined by the ground
electronic state
 The impinging projectile is considered a plane wave
The SCE method
The exchange potential: first model
The Free Electron Gas Exchange (FEGE) Potential
V
FEGE
 r    hlmV hlm
FEGE
(r ) X
A1
hlm
( ,  )
 1 1  2 1   
  K F (r )  
ln


4
1  
2
2
1/ 3
K F (r )  3  (r ) 
2
  k / KF
The SCE method
The exchange potential: second model
The SemiClassical Exchange (SCE) Potential and modified SCE (MSCE)
SCE:
 The local momentum of bound electrons can be
disregarded with respect to that of the impinging
projectile (good at high energy collisions)
The SCE method
The exchange potential: second model
The SemiClassical Exchange (SCE) Potential and modified SCE (MSCE)
MSCE:
 The local velocity of continuum particles is modified
by both the static potential and the local velocity of
the bound electrons.
The SCE method
The solution of the SCE coupled
radial equations
Once the potentials are computed, one has to solve
the integro-differential equation
The SCE method
The solution of the SCE coupled radial
equations
The quantum scattering equation single center expanded
generate a set of coupling integro-differential equation
The SCE method
The solution of the SCE coupled radial
equations
Where the potential coupling elements are given as:
The SCE method
The solution of the SCE coupled radial
equations
The standard Green’s function technique allows us to rewrite
the previous differential equations in an integral form:
This equation is recognised as Volterra-type equation
The SCE method
The solution of the SCE coupled radial
equations
In terms of the S matrix one has:
i,j identify the angular channel lh,l’h’
SCELib(API)-VOLLOC code
SCELIB-VOLLOC code
SCELIB-VOLLOC code
SCELIB-VOLLOC code
Serial / Parallel ( open MP / MPI )
SCELIB-VOLLOC code
Typical running time depends on:





Hardware / O.S. chosen
Number of G.T.O. functions
Radial / Angular grid size
Number of atoms / electrons
Maximum L value
SCELIB-VOLLOC code
Test cases:
SCELIB-VOLLOC code
Hardware tested:
Shape resonance analysis
Shape resonance analysis
 we
fit the eigenphases sum with
the Briet-Wigner formula and
evaluate G and t
Uracil
Uracil
J.Chem.Phys., Vol.114, No.13, 2001
Uracil
• ER=9.07 eV
GR=0.38 eV
t=0.1257*10-15 s
Uracil
Thymine
J.Phys.Chem. A, Vol. 102, No.31, 1998
Cubane
Cubane
Cubane
Cubane
Er=9.24 eV G=3.7 eV
t=1.8*10-16s
Cubane
Cubane
Er=14.35 eV G=4.2 eV
t=1.5*10-16s
Cubane
Conclusion and future
perspectives

Shape resonance analysis (S-matrix poles)

Transient Negative Ion Orbitals analysis (postSCF multi-det w/f)

Dissociative Attachment with charge migration
seen through bond stretching ( (R)  G(R) )

Study of the other DNA bases (thymine t.b.p.,
A,C,G planned)

Development of new codes (SCELib-API &
parallel VOLLOC)