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Quantum Chemistry: Modeling Solvation: Fe + -rare gas clusters

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### 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

- 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

- Solvation of transition metal cations by rare gas atoms. (Completed)
- Sandwich complexes of iron cations with benzene

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Current Research

- 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

- 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

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Experiment

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

MOTIVATION

Using iron pentacrbonyl co-expanded with

argon we preparedFe+Arn where the stronger Fe-

CO 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

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Similarly, magic numbers are observed for Fe+Xen ( n = 4, 6 etc.MOTIVATION

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

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.

MOTIVATIONITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Density Functional Theory

- 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

- 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

- 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

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Progress Report: Solvation of transition metal cations by rare gas atoms

- 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] + (1-A)*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

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

The B3PW91 Density Functional

- 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)

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

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

- 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.

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

RESULTS

- Spin E/Eh AE CPC ZPC-----------------------------------------------------------------

FeAr 6 -144.063358 0.073 -0.034 0.005FeAr2 6 -165.019123 0.171 -0.029 0.010FeAr3 6 -185.974387 0.188 -0.093 0.017FeAr4 4 -206.971051 0.784 -0.145 0.039FeAr5 4 -227.925696 0.804 -0.187 0.046FeAr6 4 -248.881160 0.853 -0.224 0.040FeXe 4 -138.642538 0.508 -0.022 0.009FeXe2 4 -154.158287 1.033 -0.050 0.018FeXe3 4 -169.665910 1.339 -0.075 0.025FeXe4 4 -185.173251 1.637 -0.101 0.034FeXe5 4 -200.667809 1.584 -0.129 0.036FeXe6 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

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

FeAr4, C1, E = -206.971 201, close to Td, nearly optimized, errortermination Td, E = -206.971 051 (*)FeAr5, C1, E = -227.925 666, close to C3v C3v, E = -227.925 696 (*) D3h, E = -227.917 054FeAr6, 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

ResultsITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

FeXe, C∞v, E = -138.594 589 (*)FeXe2, C2v, E = -154.158 180, close to D∞h (*) D∞h, high spin contamination, blows upFeXe3, C1, E = -169.665 910, close to C2v (*) C2v, high spin contamination, blows up

FeXe4, C1, E = -185.173 251, close to Td (*) Td, high spin contaminationFeXe5, C1, E = -200.667 809, close to C3v (*) C3v, E = -200.667 518, will not convergeFeXe6, C1, E = -216.165 920, close to Oh (*) Oh, E = -215.861 809, will not converge

ResultsITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Stability of Fe+ rare gas complexes, Fe+(Ar,Xe)n

Atomization

Energy / eV

n =

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Structure of Fe+ rare gas complexes, Fe+(Ar,Xe)n

Ar

C2v

C2v

Td

C3v

Oh

Xe

C2v

Td

C3v

Oh

n = 1 2 3 4 5 6

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

Conclusions

- 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

- 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.

ITR-BioGeometry Meeting, Nov. 14, 2002, Chapel Hill, NC

FUTURE DIRECTIONS

- 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

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