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 • pK a (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, J AB – 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 AH n – LiH, BeH 2 , BH 3 , BH 4 – , CH 4 , NH 3 , NH 4 + , OH 2 , FH – NaH, MgH 2 , AlH 3 , AlH 4 – , SiH 4 , PH 3 , PH 4 + , SH 2 , ClH • Simple A-B bonded systems H m A-BH n – H 3 C-CH 3 , H 2 N-NH 2 , HO-OH, F-F – H 3 C-NH 2 , H 3 C-OH, H 3 C-F, etc.

• Multiple bonded AB systems ABH n

Beyond Minima: Reactions • Potential Energy Surfaces • Transition Structures • Reaction Paths • Transition States • Reaction Rates

Generic Textbook Reaction Path Usually for unimolecular processes • 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?

E n e r g y - - >

TS ² E a Reactant(s) ² E rxn Product(s)

Reaction Coordinate -->

Simplest P.E. Curve: Diatomics • Diatomic dissociation is familiar • Linear structure: 3n-5 =1 mode • Reaction Coord. is uniquely defined as r(A…B)

E n e r g y - - >

A –B

Reaction Coordinate -->

A + B ² E of diatomic dissociation

Generic Reaction Path Common for bimolecular processes • In gas phase, two fragments always “stick” together a bit. TS Separated Reactants • TS may be above or below fragment totals.

² E assn

E n e r g y - - >

² E a ² E overall Separated Products ² E dissn • Minima may have inverse E order e.g. H 3 O – Reactant Complex ² E rxn Product Complex

Reaction Coordinate -->

Rxn Paths: TS Vibrational Modes Vibrations in the TS for the (degenerate) S N 2 attack of Cl – on CH 3 Cl. Note: all but the Reaction Coord motion are positive “ordinary” vibrations 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.

The Transition Structure • Stationary Point (i.e. gradients ~ 0) • One imaginary frequency (“Nimag=1”) • Locate by minimizing gradient (  E/  x i ) • 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

g x

0,

g y

=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.