CEM 888: Molecular Modeling: Applications for Experimentalists

What can theory do for the practicing chemist? What do we wish it could do? A brief progress report with examples

on the performance and practical utility of theoretical tools for non-theoreticians

The Evolving Roles of Theory

Pattern-matching–>Explanatory–>Exploratory–>Predictive–>Prescriptive?

• Organize data around common themes• Develop physical insights into data• Interpolate and extrapolate from data to

analogous systems• Predict results for proposed new expts• Identify and propose new experiments

Wish List (add items as desired)

Zeroth order wishes:

• Theory should always get the answer right

• Should be applicable to “real” molecules, materials, and situations

• Should teach us something so we can better think about science (who wants to always need a supercomputer in their back pocket?)

Chemistry Wishes: Structure

• Internal: distances, angles, dihedrals

• Rotational constants and symmetry

• Conformational preferences

• Solvation sphere

• Lattice packing

• Sensitivity to environment (solvent, pressure, fields, etc.)

Chemistry Wishes: Energetics

• Heats of formation• Isomer relative energies• “Effect” energies: strain, aromaticity, solvation, etc.• Heats of fusion, vaporization; heat capacities• Ionization potentials/e– affinities

– UPS/XPS, E-chem, redox reagent chemistry

• Bond strengths, atomization energies – MS, reaction paths

Chemistry Wishes: Observables

• Melting and boiling points• Density, viscosity• Refractive index, optical rotation, CD/ORD• Solubilities in various solvents• pKa (or other ionic dissociation abilities) • Dipole, polarizability• Magnetic susceptibility and e–-e– coupling

Chemistry Wishes: Spectroscopies

• UV-vis-IR/Raman-µwave absorption/emission– Peak positions– Transition intensities, rates (Abs, ISC, Emission, Internal conv.)

• NMR – Chemical shifts, – Spin-spin couplings, JAB

– Relaxation times– NOE intensities– Conformational dynamics

• EPR– Spin densities– Hyperfine coupling constants

Chemistry Wishes: Reactivity and Mechanism

• Activation parameters• Transition state structures and reaction paths• Conformational interconversion barriers (NMR)• Isotope effects• Solvent effects on all (structure, energetics, etc.)

Chemistry Wishes: New Insights

• Charge allocation to atoms--meaningful?• Why aren’t some classically valid-looking

structures stable?• Are orbitals or resonance structures “real”?• How about “ring currents”• “Steric” vs. “Electronic” effects• VSEPR?

Performance of the Methods: Structure

• “Ordinary” compounds--simple hydrides AHn

– LiH, BeH2, BH3, BH4–, CH4, NH3, NH4

+, OH2, FH– NaH, MgH2, AlH3, AlH4

–, SiH4, PH3, PH4+, SH2, ClH

• Simple A-B bonded systems HmA-BHn

– H3C-CH3, H2N-NH2, HO-OH, F-F– H3C-NH2, H3C-OH, H3C-F, etc.

• Multiple bonded AB systems ABHn

Beyond Minima: Reactions

• Potential Energy Surfaces

• Transition Structures

• Reaction Paths

• Transition States

• Reaction Rates

Generic Textbook Reaction PathUsually for unimolecular processes

TS

Reactant(s)

Product(s)

∆Ea

∆Erxn

Reaction Coordinate -->

• How are stationary points and reaction path defined?

• Are they unique and independent of coordinate system?

• What is a “Reaction Coordinate” anyway, in 3n-6 dimensions?

Simplest P.E. Curve: Diatomics

• Diatomic dissociation is familiar

• Linear structure:3n-5 =1 mode

• Reaction Coord. is uniquely defined as r(A…B)

Reaction Coordinate -->

∆E of diatomicdissociation

A–B

A + B

Generic Reaction PathCommon for bimolecular processes

• In gas phase, two fragments always “stick” together a bit.

• TS may be above or below fragment totals.

• Minima may have inverse E order e.g. H3O–

TS

ReactantComplex

ProductComplex

∆Ea

∆Erxn

Reaction Coordinate -->

∆Eassn

SeparatedReactants

SeparatedProducts

∆Edissn

∆Eoverall

Rxn Paths: TS Vibrational Modes

From Anwar G. Baboul and H. Bernhard Schlegel, “Improved method for calculating projected frequencies along a reaction path” J. Chem. Phys. 1997, 107, 9413-9417.

Vibrations in the TS for the (degenerate) SN2 attack of Cl– on CH3Cl. Note: all but the Reaction Coord motion are positive “ordinary” vibrations

The Transition Structure

• Stationary Point (i.e. gradients ~ 0)

• One imaginary frequency (“Nimag=1”)

• Locate by minimizing gradient (E/xi)

• Structure is independent of coordinate system, nuclear masses

• Is this structure the transition “state”?

• How to get close enough for local optimiz’n

Searching for the MEP or IRC• At the TS only, the reaction coord is well defined,

as the mode with the imaginary freq.• From TS, follow steepest descent at each step.• Reaction path points not independently defined;

path curves (i.e. rxn coord makeup varies)• Search scheme, step

size, intermediate optimization are all important.

Sample PES

Anglada, J. M.; Besalú, E.; Bofill, J. M.; Crehuet, R.J. Comput. Chem. 2001,

22, 387-406.

Figure 9. The Müller-Brown potential surface. Dashed line, energy contours. Solid line is the reduced potential surface defined as gx0, gy=0. The black circles are the stationary points, minimum, M1 and M2, transition state, TS1. The empty circles are the starting point, P, and the turning point, TP. The black dots are the different points evaluated by the algorithm; see text for more details.