Boosting an old method with a new
basis: MP2 electron correlation
Andrea Sanfilippo, X.Ren, P. Rinke, V. Blum, K.Reuter,
M. Scheffler
Fritz-Haber Institut der Max-Planck
Gesellschaft
About me…
Andrea Sanfilippo
2004
Degree in Material Science at the
Milano-Bicocca University
Thesis project:
Construction of an ab-initio Green
function code for non-periodical
systems using an Embedding
Method (supervised by Trioni,
Brivio)
2005/ 2006
Doctoral project at the University
College of London:
Hybrid computational method for
scattering of elastic waves in Metal
Matrix Composites
Since January 2007 at the at Fritz-Haber Institut in
Berlin:
PhD on ab-initio study of Surface Molecular
networks
Introducing Electronic Structure
Theory
Modern ab-initio methods in the BornOppenheimer approximation:

i.
ii.


wave function (Hartree-Fock, post-HF, QM)
density functional methods (DFT)
Present day DFT functionals and wave function
based methods treat accurately bonded systems
like metals, semiconductors, molecules…
but…in nature weak interactions are widespread
(physisorption, protein folding, glues etc.)
How do we treat their ground states accurately and
efficiently?
DFT in brief , the Kohn-Sham trick
?



Exact Exc unknow, is guessed (often parametrized)
i.
local (TF, LDA): local density of homogenous
and isotropic electron gas approximation
ii.
semi-local (GGAs): gradient expansions on LDA
iii.
non-local (OEP, HyFs, vdW): hybrid density/w.f.
to recover long-range physical effects
There is not (yet) a systematic way to treat weak
bonded systems
Computationally fast ~ O(N3), N number of basis
E : Ground state energy, TS : Kinetic energy of the free electrons, VII : Nuclear interactions
The grand-father method of quantum
chemistry : Hartree-Fock (1930)

Hartree-Fock approximation

approximation: only Pauli principle considered, but
it is a poor approximation, what is missing is called
correlation
e- dig a hole around himself (like exact solution)

e-
e-
: Fermi energy, V : Coulomb potential, n : density, VH Hartree potential
Perturbation theory: MP2 (1934)

The second order of perturbation is a first
estimation of correlation between two particles

Computation expensive ~ O(N5):
Basis set to expand MO:

i.
ii.

terms
Gaussian or Slater type basis set
Numerical Atomic Orbitals (NAO)
Gaussian generally used so far, to make it faster
N : number of atomic basis functions, i,j : molecular orbitals label (spin included)
Two basis set in comparison
Gaussian:
i.
Localize basis set
ii.
Analytical integrals
iii.
Many functions required to recover physics
iv.
Construction problematic for heavier elements
 Numerical atomic orbitals
i.
Localized basis set
ii.
Numerical integration
iii.
Correct physics recovered
few functions!
iv.
Can be more easily generated

Aim of the project



Implementation of second order many body
perturbation theory using numerical atomic orbital
code using
Describe weak bonded systems efficiently with the
highest accuracy
Applications: weak molecular bonds, extended
systems in presence of heavy elements, surface
physisorption
To improve scaling and timing

Resolution of identity defined as projector
giving a computationally cheaper term

In density fitting we introduce an auxiliary basis set
the residual
depending on the metric.
can be minimized
Vahtras, Almlof, Feyereiesen (1993) . Mulliken notation applied :
Main Features of RI/DF-MP2



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Auxiliary basis set taken generally as m ~ N
Number of calculations ~ O(mN4), but
computing time <10% than full-MP2 and storage
can be reduced to ~ O(mN2)
RI-MP2 size consistent
Resulting error lower than the basis set error
(error due to incompleteness of basis set, i.e.
BSSE)
Weigend et al. (2002) Weigend et al. (2002), Weigend (2006) , Sodt et al. (2006)
What we have done so far…
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
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RI-MP2 is feasible with NAO
Development of parallel RI-MP2 and BSSE correction
using a NAO in-house code, “FHI-aims”
Basis set study starting from MP2 or DFT-LDA
Applied to small molecules and Hydrogen bonded
system with accurate results
… and future
further optimizations (matrix sparsity, PB …) and
application to a wider range of practical systems,
adsorption on surfaces in particular
The FHI Ab Initio Molecular Sim. (aims) project, www.fhiberlin.mpg.de/aims/
Few examples…
Water dimer (PBE optimized geometries)
O2
NAO basis set applied here are LDA optimized
Thanks!
Aknowledgements:
MONET - Molecular Networks at Phase Boundaries
Marie Curie Early Stage Researcher Training Network
The FHI Ab Initio Molecular Simulations (aims) project
V. Blum and M. Scheffler; R. Gehrke, P. Havu, V. Havu, X. Ren, A. Sanfilippo, F.
Hanke, A. Tkatchenko, P. Rinke, and K. Reuter.
www.fhiberlin.mpg.de/aims/