Transcript Quantum Chemistry

Quantum Chemistry:
+
Modeling Solvation: Fe rare gas clusters
Solomon Bililign
Department of Physics
North Carolina A&T State University
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Members
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Solomon Bililign PI
Robert Gdanitz: Senior Research Scientist
Kevin Wedderbrun: Graduate Student
Sewyalew Tadelle: Undergraduate Student
Nayana Vaval: Former Postdoc
Zaki Abdulrahman: Former Graduate Student
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Current Research
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Solvation of transition metal cations by
rare gas atoms. (Completed)
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Sandwich complexes of iron cations
with benzene
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Current Research
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The reaction of transition metal cations with small
aliphatic hydrocarbons:The reaction of cationic Fe
and Cr clusters with small aliphatic hydrocarbons
(e.g. CH4, C2H2, C2H4) is of particular interest
because the metals may catalyze fusion reactions
that yield larger hydrocarbons. One pertinent
example is the cyclo-trimerization of ethine (C2H2)
to benzene, which is catalyzed by Fen+ clusters
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Current Research
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Quenching of excited Li by gases:alkanes like
C2H6, and C3H8 and Alkenes: C2H4
The ability of alkanes like C2H6, and C3H8 to
quench an (excited) Li* atom depends on the state
of the latter. The complete interpretation of our
experiments requires extensive computations of
the potential energy surfaces in order to gain
insight in the reaction mechanisms (which are not
obvious in this case) and in the relative energetics.
We are further interested in the interaction of Li*
with alkenes like C2H4 (which is an active
quenching agent).
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Experiment
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2002, Chapel Hill, NC
Experiment
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
MOTIVATION
Using iron pentacrbonyl co-expanded with
argon we prepared Fe+Arn where the stronger FeCO bonds have been photolyzed but some fraction of
the argon solvent is retained. We have found that
metal-metal clustering is severely limited with 266
nm MPI of Fe(CO)5 we have instead found that these
conditions generate Ar solvated metal ions.
The main cluster series in the mass spectrum
are Fe+Arn which is the strongest followed by
Fe(CO) +Arn and Fe2+Arn. To form these ions
requires that the argon solvent be at least
partially retained while the Fe(CO)5 is striped
of its CO ligands. This is surprising since
during this process the strong bonds are being
broken but the weak ones are retained.
Additionally a very large magic number is
observed at n = 6 in the Fe+Arn series
indicating that the preferred geometry for Ar
solvation of Fe+ is octahedral
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2002, Chapel Hill, NC
MOTIVATION
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Similarly, magic
numbers are observed
for Fe+Xen ( n = 4, 6
etc.
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2002, Chapel Hill, NC
MOTIVATION
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When iron pentacrbonyl
was co-expanded with
benzene in argon carrier
gas we observed Fe+(C6H6)n
where benzene,which
fragments extensively
under these MPI
conditions, is stabilized by
the presence of metal.
Our data show a fairly
strong peak at Fe2+ (bz)3,
which may be the first
observation of this for Fe-bz
systems.
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Density Functional Theory
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In recent years Density Functional Theory (DFT) has
become the most popular method in quantum
chemistry.
The reason for this preference is the extreme
computational cost required to obtain chemical
accuracy with multiple determinant methods.
This difference in speed is heightened by the fact that
multiple determinant calculations require very large
basis sets, with high momentum basis functions,
whereas DFT can produce accurate results with
relatively small basis sets.
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Density Functional Theory
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In DFT, the derivation begins with the total energy written as
a functional of the total electron density for given positions of
the atomic nuclei.
In contrast to HF, DFT used a physical observable: The
electron density as a fundamental quantity.
In HF the total energy is expressed as an expectation value of
the exact non-relativistic Hamiltonian using Slater determinant
as an approximation for the total wave function. In DFT, the
total energy is decomposed in a formally exact way into three
terms Kinetic energy term T [r], electrostatic or Coulomb
energy term U[r] and many body exchange term EEX[r],
which includes all exchange and correlation effects
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Density Functional Theory
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E = T [r], + U[r] + EEX[r],
T[r] corresponds to the kinetic energy of a system on
non-interacting particles that yield the same density
as the original electron system
Total density is decomposed into single-particle
densities which originate from one-particle wave
functions
r = occ yi(r )2
DFT requires that upon variation of total electron
density, the total energy assumes a minimum
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2002, Chapel Hill, NC
Progress Report: Solvation of transition metal
cations by rare gas atoms
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B3PW91:Becke Perdew and Wangs gradient
corrected correlation density functional implemented
via Gaussian 98 is used.
To save computer time: pseudo-potentials are used as
basis set (the LANL2DZ: the scalar relativistic
pseudopotential developed by Los Alamos Nat’l Lab)
The Boys-Bernardy couterpoise corrections did not
change much indicating the choice of basis set is
appropriate.
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
The B3PW91 Density Functional
E = T[orb] + V[r] + A*Ex[Slater] + (1A)*Ex[HF] + B*D Ex[Becke] + Ec(VWN] +
C*DEc(PW]
Where
T[orb]: Kinetic energy computed as a function of
orbitals
V[r]: Coulomb self-energy of the electronic
charge distribution
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2002, Chapel Hill, NC
The B3PW91 Density Functional
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Ex is the exchange energy
Ex(HF) is the Hartree-Fock exchange energy
DEx(Becke): Correction to the exchange
energy
Ec: Correlation energy
Ec(VWN) is the Vosko, Wilk and Nusair 1980
fit to uniform electron gas model
DEc(PW): is the gradient correction
(depending on grad r(r) of Perdew and Wang)
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Method
For each of the M+Xn clusters many initial configurations were tried and based on minimum
energy and atomization energy calculations most stable structures were obtained. Atomization
energies [energy difference between molecule and component atoms] calculated w/r/t to
Fe+ in the same spin multiplicity as the complex using ,
Do = [EA(A) + EB(B)] – [EAB(AB)+ZPC]
(1)
Where, EA(A) and EB(B) are the monomer energies using the respective monomer basis sets,
EAB(AB) is the total energy of the complex AB at the geometry of AB using entire basis set.
Atomization energy is calculated with un-scaled zero point corrections. BSSE corrections are
obtained using following equation
DCCo = [EA(G,AB) + EB(G,AB)] – [EAB(G,AB)+ZPC]
(2)
Where, EA(G, AB) and EB(G, AB) denote the energy of the monomer A and B at the
geometry G (geometry of the complex AB) with the basis set of AB. In the calculation
of EA(G,AB) the basis set of B is present but the nuclei of B are not.
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Progress Report: Solvation of transition metal
cations by rare gas atoms
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Due to large number of low lying excited
states for transition metals, the computations
are generally difficult.
Due to the unrestricted nature of the
functionals, and due to the inability of
Gaussian to exploit non- abelian point groups,
spin and spatial symmetry breaking took place.
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2002, Chapel Hill, NC
RESULTS
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Spin
E/Eh
AE
CPC
ZPC
----------------------------------------------------------------FeAr 6 -144.063358 0.073 -0.034 0.005
FeAr2 6 -165.019123 0.171 -0.029 0.010
FeAr3 6 -185.974387 0.188 -0.093 0.017
FeAr4 4 -206.971051 0.784 -0.145 0.039
FeAr5 4 -227.925696 0.804 -0.187 0.046
FeAr6 4 -248.881160 0.853 -0.224 0.040
FeXe 4 -138.642538 0.508 -0.022 0.009
FeXe2 4 -154.158287 1.033 -0.050 0.018
FeXe3 4 -169.665910 1.339 -0.075 0.025
FeXe4 4 -185.173251 1.637 -0.101 0.034
FeXe5 4 -200.667809 1.584 -0.129 0.036
FeXe6 4 -216.165920 1.620 -0.166 0.012
-----------------------------------------------------------------Energies in eV.
AE: Atomization energy, CPC:counterpoise correction ,ZPC:zero-point corrections
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Results
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Excitation energy Fe+, sextet ->
quartet: -0.56 eV (exp., averaged
over multiplets: 0.25 eV)
FeAr, C∞v, E = -144.063 358 (*)
FeAr2, C2v, E = -165.019 123 (*)
D∞h, E = -164.247 539
FeAr3, C2v, E = -185.974 387 (*)
D3h, E = -185.973 159
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FeAr4, C1, E = -206.971 201, close
to Td, nearly optimized, error
termination
Td, E = -206.971 051 (*)
FeAr5, C1, E = -227.925 666, close
to C3v
C3v, E = -227.925 696 (*)
D3h, E = -227.917 054
FeAr6, C1, E = -248.878 303, close
to D3h
D3d, E = -248.881 160 (*)
D4h, blows up
D3h, high spin contamination,
blows up
Oh, blows up
ITR-BioGeometry Meeting, Nov. 14,
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Results
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FeXe, C∞v, E = -138.594
589 (*)
FeXe2, C2v, E = -154.158
180, close to D∞h (*)
D∞h, high spin
contamination, blows up
FeXe3, C1, E = -169.665
910, close to C2v (*)
C2v, high spin
contamination, blows up
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FeXe4, C1, E = -185.173
251, close to Td (*)
Td, high spin
contamination
FeXe5, C1, E = -200.667
809, close to C3v (*)
C3v, E = -200.667 518,
will not converge
FeXe6, C1, E = -216.165
920, close to Oh (*)
Oh, E = -215.861 809,
will not converge
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Stability of Fe+ rare gas complexes,
Fe+(Ar,Xe)n
Atomization
Energy / eV
2
1.5
1
Ar
Xe
0.5
0
n=1 2
1
2
3 4
3
5
4
6
5
6
Ar 0.07 0.17 0.19 0.78 0.8 0.85
Xe 0.51 1.03 1.34 1.64 1.58 1.62
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Structure of Fe+ rare gas complexes,
Fe+(Ar,Xe)n
Ar
C∞v
C2
C2v
Td
C3v
Oh
D∞h
C2v
Td
C3v
Oh
2
3
4
5
6
v
Xe
n
C∞v
= 1
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
Conclusions
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DFT is moderately accurate and is not a high
precision method (Kohn)
More accurate methods for such systems are
prohibitively expensive, thus DFT is a method of
choice.
The calculations confirm the observation that n = 4
and 6 are magic numbers for Fe+Xen clusters.
The calculations also confirm our postulate that the
Fe+RG6 clusters have an octahedral structure.
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC
EDUCATION
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Group plays a central role in the creation of a
graduate degree program in Computational Sciences
in collaboration with the Departments of Chemistry,
Biology, Mathematics and Computer Science at A&T.
Feasibility study completed with fund from Sloan
Foundation.
New courses both graduate and undergraduate
entitled: Computational methods in physical and
biological sciences under development.
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2002, Chapel Hill, NC
FUTURE DIRECTIONS
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Prediction of Molecular Crystal Structures – Proposed
Research
Gdanitz Monte-Carlo software: Accelrys’ “Polymorph
Predictor” in Cerius2 for ≈ $70,000(?)
Not sold to academia(!)
To do: Interface code with common non-commercial molecular
modeling software
Already done: Advanced code in collaboration with
Hoechst/Frankfurt interfaced with “Molmec”
Further possibilities: “Mutate” algorithm to solve pertinent
global energy minimization problems, e.g. protein folding
Search for collaborations within BioGeometry Group
ITR-BioGeometry Meeting, Nov. 14,
2002, Chapel Hill, NC