Download The Aromatic Character of Substituted Tria

Computational Chemistry for
Dummies
Svein Saebø
Department of Chemistry
Mississippi State University
Computational Chemists /
Theoretical Chemists

Computational Chemists use existing
computer software (often commercial) to
study problems from chemistry
 Theoretical Chemists develop new
computational methods and algorithms.
Theoretical / Computational
Chemistry
Tool: Modern Computer
 Application of

– Mathematics
– Physics
– Computer Science
– to solve chemical problems
Chemistry

Molecular Science
– Studies of molecules

Large Molecules, macromolecules:
– Proteins, DNA
 Biochemistry, Medicine, Molecular Biology
– Other polymers
 Material Science (physics)
Computational Chemistry

WHY
– do theoretical calculations?

WHAT
– do we calculate?

HOW
are the calculations carried out?
WHY?

Evolution of Computational Chemistry
– Confirmation of experimental results
– Interpretation of experimental results

assignment
– Prediction of new results
– The truth is experimental!

Advantages
– Avoid experimental difficulties
– Safety
– Cost

Widely used by chemical and pharmaceutical industry
– Visualization
WHAT?

Molecular System
– One or several molecules

Collection of atoms
 Structure (geometry):
– 3-dimensional arrangement of these atoms
WHAT?
Molecular Potential Surfaces
 A molecular system with N atoms is described by
3N Cartesian (x,y,z) or 3N-6 internal coordinates
(bond lengths, angles, dihedral angles)

– R = {q1 ,q2 ,q3 q4 ,….. q3N-6}

Potential Energy Surface (PES) : E(R)
– the energy as a function of the three-dimensional
arrangement of the atoms.
Diatomic Molecule

Only one coordinate:R= bond length
– Potential Surface: E(R)
E(R)

Morse Potential:
 Parabola:
 First derivative:
 Second derivative
E=D(1-exp(-F(R-R0))2
E=1/2 F (R-R0)2
dE/dR = F (R-R0)
d2E/dR2 =F
– (force-constant, Hooks Law)

Vibrational Frequency n=1/(2p) (F/m)
Intercept through a PES.

Stationary points
– Minima
– Saddle points (transition states)
Potential Surfaces

We are normally interested in stationary
points
– Global Minimum : Equilibrium Structure
– Local Minima: Other (stable?) forms of the
system
– Saddle Points: Transition States
Stationary Points

Mathematical Concept
dE / dqi = 0 for all i
Slope of potential energy curve = 0

Minimum: second derivatives positive
 Maximum: second derivatives negative
 Saddle Point: All second derivatives
positive except one (negative)
WHAT do we calculate?
Energy:
E(q1,q2,q3,….q3N-6)
 Gradients:
dE/dqi
 Force Constants:
Fi,j = d2E/dqidqj
 + Other second derivatives with respect to

–
–
nuclear coordinates
electric , magnetic fields
Gradients (dE/dq)

Needed for automatic determination of
structure
 Force (f) in direction of coordinate q
– f = -(dE/dq) = -F (R-R0)

Geometry relaxed until the forces vanish
– Quadratic surface:
R+ f/F=R-F(R-R0)/F=R0
Force Relaxation:
(1) start with an initial guess of the geometry Rn
and the force constants F (a matrix) (n=1)
 (2) calculate the energy E(Rn), and the gradient
g(Rn) at Rn
 (3) get an improved geometry:

– Rn+1 = Rn –F-1 g(Rn)

(4) Check the largest element of g(R)
– If larger than THR (e.g. 10-6) n=n+1 go to (2)
– If smaller than THR – finished

The final result does not depend on F
Optimization Methods

Calculation of the gradient at several
geometries provide information about the
force-constants F
 Widely used optimizations methods:
–
–
–
–
Newton Raphson
Steepest Decent
Conjugate gradient
Variable Metric (quasi Newton)
WHY Second Derivatives?

provide many important molecular(spectroscopic)
properties
– Twice with respect to the nuclear coordinates

F=d2E/dqidqj Force Constants Vibrational Frequencies
– Dipole moment derivatives  IR intensities
– Polarizability Derivatives  Raman Intensities
– Once with respect to external magnetic field, once with
respect to magnetic moment.

Magnetic shielding- chemical shifts (NMR)
Summary (What?)

Common for all Computational chemistry
Methods:

Potential Energy Surfaces
– Normally seeking a local minimum (or a saddle point)
– Get energy and structure

Spectroscopic properties are normally only
calculated by quantum mechanical methods
HOW?

How do the computer programs work?
– Many different computational chemistry programs
– Wide range of accuracy


Low price - low accuracy
User Interface
– Input/output
– Many modern programs are very user friendly

menu-driven point and click
HOW?

Molecular Mechanics
– Based on classical mechanics
– No electrons or wave-function
– Inexpensive; can be applied to very large
systems (e. g. proteins)

Quantum Mechanical Methods
– Seek approximate solutions of the Schrödinger
equation for the system HY = E Y
Quantum Mechanical Methods

Exact solutions only for the hydrogen atom
–

s, p, d, f functions
Molecules: LCAO-approximation
– fi = S CimCm
– {C} H-like atomic functions: Basis set (AO)
– {f} Molecular orbitals (MO)
Quantum Mechanical Methods

Semiempirical Methods
– Use parameters from experiments
– Inexpensive, can be applied to quite large
systems

Ab Initio Methods
– Latin: From the beginning
– No empirical data used [except the charge of
the electron (e) and the value of Planck’s
constant (h)]
Semi empirical Methods

p-electrons only
– Hückel, PPP (Pariser Parr Pople)

Semi empirical MO methods
– Extended Hückel
– CNDO, INDO, NDDO
– MINDO, MNDO,AM1,PM3…(Dewar)
Ab Initio Methods

Hartree-Fock (SCF) Method
– based on orbital approximation
– Single Configuration
 Wave-Function:Y a single determinant
– Each electron is interacting with the average of
the other electrons
– Absolute Error (in the energy) : ~1%
– Formal Scaling : N4 (N number of basis
functions)
Ab Initio Methods

Electron Correlation
– Ecorr = E(exact) - EHF
– Many Configurations (or determinants)
– MP2-scale as N5
– CI, QCISD, CCSD, MP3, MP4(SDQ) - scale as N6
Power-Law Scaling

Ab Initio Methods: N4 – N6
– N proportional to the size of the system
– Double the size: Price increases by a factor of
~60! (from 1 minute to 1 hour)
– Increase computational power with a factor of
1000
– 1000 ~ 3.56
– Could only do systems 3-4 time as big as today
The Future of Quantum
Chemistry

Dirac (1929):
– “The underlying physical laws necessary for the
mathematical theory of the whole of chemistry are thus
completely known, and the difficulty is only that the
exact application of these laws leads to equations much
too complicated to be soluble”
– 1950’s
“it is wise to renounce at the outset any attempt at
obtaining precise solutions of the Schrodinger equation
for systems more complicated than the hydrogen
molecule ion”
Levine: “Quantum Chemistry”
Fifth Edition
Future of Quantum Chemistry

The difficulties at least partly overcome by
application of high speed computers
 1998 Nobel Price Committee: (Chemistry Price
shared by Walter Kohn and John Pople):
– “Quantum Chemistry is revolutionizing the field of
chemistry”

We are able to study chemically interesting
systems, but not yet biologically interesting
systems using quantum mechanical methods.
Low-Scaling Methods for
Electron Correlation

Low Scaling MP2
– Near linear scaling for large systems
– formal scaling N5
– Applied to polypeptides (polyglycines up to 50
glycine units, C100H151N50O51)


Saebo, Pulay, J. Chem. Phys. 2001, 115, 3975.
Saebo in: “Computational Chemistry- Review of
Current Trends” Vol. 7, 2002.
Molecular Mechanics

Based on classical mechanics
 No electrons or wave-function
 Inexpensive; can be applied to very large
systems, macromolecules.
– Polymers
– Proteins
– DNA
Molecular Mechanics

E=Estr + Ebend + Eoop + Etors + Ecross + EvdW +
Ees
–
–
–
–
–
Estr
Ebend
Eoop
Etors
Ecross
bond stretching
bond-angle bending
out of plane
internal rotation
combinations of these distortions
– Non-bonded interactions:
– EvdW van der Waals interactions
– Ees
electrostatic
Force Fields

The explicit form used for each of these
contributions is called the force field.

Will consider bond stretching as an example
Bond Stretching

E(R)=D (1-exp(-F(R-R0))2

D - dissociation energy
 F - force-constant
 R0 - ‘natural’ bond length
 The parameters D, F, R0 are part of the so-called
force-field.
– The values of these parameters are determined
experimentally or by ab initio calculations
Force-fields

Similar formulas and parameters can be
defined for:
– Bond angle bending
– Out of plane bending
– Twisting (torsion)
– Hydrogen bonding , etc.
Molecular Mechanics
Force-fields

Each atom is assigned to an atom type
based on:
– atomic number and
– molecular environment

Examples:




Saturated carbon (sp3)
Doubly bonded carbon (sp2)
Aromatic carbon
Carbonyl carbon…..
Force-fields

An energy function and parameters (D, F,
R0) are assigned to each bond in the
molecule.
 In a similar fashion appropriate functions
and parameters are assigned to each type of
distortion
 Hydrogen bonds and non-bonding
interactions are also accounted for.
Commonly Used Force Fields

Organic Molecules:
– MM2, MM3, MM4 (Allinger)

Peptides,proteins, nucleic acids
– AMBER (Assisted Model Building with
Energy Refinement) (Kollman)
– CHARMM (Chemistry at HARvard Molecular
Modeling (Karplus)
– MMFF94 (Merck Molecular Force Field)
(Halgren)
More Force Fields..

CFF93, CFF95 (Consistent Force Field)
– Hagler (Biosym, Molecular Simulations)

SYBYL or TRIPOS (Clark)
Computational Chemistry and
NMR

Powerful technique for protein structure
determination competitive with X-ray
crystallography.
 NOE: Nuclear Overhauser Effect
– Proton-proton distances
– Structure optimized under NOE constraints
– Chemical shifts are also used
Protein G
Angela Gronenborn, NIH
5-Enolpyruvylshuikimate-3phosphate Synthase
Acknowledgements

Dr. John K.Young, Washington State
University