©2013, jordan, schmidt & kable lecture 16 lecture 16 molecular structure and thermochemistry...

©2013, Jordan, Schmidt & Kable Lecture 16

Lecture 16 Molecular Structure and Thermochemistry

Structure = min[f(x1,y1,z1,…xN,yN,zN)]


Copyright Notice

Some images used in these lectures are taken, with permission, from

“Physical Chemistry”, T. Engel and P. Reid, (Pearson, Sydney, 2006);denoted “ER” throughout the lectures

and other sources as indicated, in accordance with the Australian copyright regulations.


16.1 Recall that equilibrium geometries can be calculated by minimizing the energy, often using Newton’s method.

16.2 Know that the calculated geometries and energies depend on the basis sets used and the level of correlation.

16.3 Recognize MP2 as a method that can recover correlation for ground states, but is not variational.

16.4 Recognize G1, G2 and G3 as composite methods which try to get to “chemical accuracy” – 1 kcal/mol

Learning outcomes


The adiabatic Born-Oppenheimer approximation

Curves like this form a landscape on which molecules vibrate and react.

Implicitly, we assume that the electrons instantaneously adapt to the positions of the nuclei. This is the adiabatic Born-Oppenheimer approximation.

This approximation is the foundation of chemical physics, and only breaks under certain circumstances, for instance where two electronic states are close in energy.

Internal conversion is an example of Born-Oppenheimer breakdown.

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2

-1.18

-1.16

-1.14

-1.12

-1.10

-1.08

-1.06

-1.04

-1.02

-1.00

-0.98

-0.96

-0.94

-0.92

-0.90

Ene

rgy

(har

tree

)

H-H distance (Å)


Potential energy surfaces – electronic states

Here are pictured the various low-lying electronic states of C2. Each has its own potential energy curve and is described well by one configuration at equilibrium. However, as the molecule dissociates, there are many instances where CI is important.

The emission from d to a is responsible for the blue coloration of lean flames and was observed in comets since the 19th century. Scott will teach you all about that stuff.


Potential energy surfaces – reactions

Here is pictured the classic potential energy surface (PES) for a linear harpoon reaction with a barrier: A + BC→AB + C.

The reaction barrier appears as a mountain pass, and is called a saddle point – it has one direction with negative curvature, like a saddle.If the PES is known with sufficient accuracy, then dynamical calculations can be made which predict the outcome of chemical reactions. Meredith like this. Scott likes Meredith doing this.


Contour Plots of acetylene H-C☰C-H

Excited state acetylene

Ground state acetylene(draw yourself)


Very strange world of Jahn-Teller

In the E” excited state of phenalenyl radical, there are e’ vibrational modes which lift the electronic degeneracy. The potential energy surface splits into two at a conical intersection. An adiabatic walk around the conical intersection accompanies a change in sign of the electronic wavefunction… BO approximation is completely broken here. (Tim likes doing this…)


Energy Minimization

Classically speaking, the structure of a molecule at 0K can be described by the minimum energy on the electronic ground state potential energy surface.

This is the minimum of the electronic energy PLUS the nuclear repulsion energy.

Minimum energy for water is here:

an

gle

ROH


Energy Minimization

If gradients are available, then the minimum can be found quickly using Newton’s method, solving for dV/dq = 0

NSERCH= 0 ENERGY= -75.8864335 NSERCH= 1 ENERGY= -75.9452753 NSERCH= 2 ENERGY= -76.0012472 NSERCH= 3 ENERGY= -76.0060757 NSERCH= 4 ENERGY= -76.0109427 NSERCH= 5 ENERGY= -76.0109543 NSERCH= 6 ENERGY= -76.0109546

----------------------- GRADIENT (HARTREE/BOHR) ----------------------- ATOM ZNUC DE/DX DE/DY DE/DZ -------------------------------------------------------------- 1 O 8.0 0.0000000 0.0000000 -0.0000514 2 H 1.0 0.0000000 0.0000176 0.0000257 3 H 1.0 0.0000000 -0.0000176 0.0000257

MAXIMUM GRADIENT = 0.0000514 RMS GRADIENT = 0.00002251 ***** EQUILIBRIUM GEOMETRY LOCATED *****

COORDINATES OF ALL ATOMS ARE (ANGS) ATOM CHARGE X Y Z ------------------------------------------------------------ O 8.0 0.0000000000 0.0000000000 -0.0470528019 H 1.0 0.0000000000 -0.7832785007 -0.5764735991 H 1.0 0.0000000000 0.7832785007 -0.5764735991

Starting at wrong geometry, convergence in just 6 steps. (RHF/6-311G)


Geometry depends on basis set

Since the energy depends on the basis set, so does the potential energy surface and thus so does the equilibrium geometry.

Method Bond length

angle Energy (Eh)

RHF/STO-3G 0.9894 100° -74.9659

RHF/3-21G 0.9667 108° -75.5860

RHF/6-31G 0.9497 112° -75.9852

RHF/6-311G(d,p)

0.9411 105° -76.0471

MP2/6-311G(d,p)

0.959 102° -76.2679 Spectroscopic determination


What is MP2?

MP2 is a non-variational theory which takes account of excited determinants (correlation) in the ground state wavefunction using second order perturbation theory.

It is named for Moller and Plesset who published the original idea.

It is based on Raleigh-Schrödinger perturbation theory (RS-PT). This theory makes use of the fact that corrections to the wavefunction are small in order to make a first order correction to the wavefunction, which gives a second order correction to the energy.

The calculation will fail if the ground state is not dominated by a single configuration.


Geometry depends on level of theory

Since the energy depends on the level of theory, so does the potential energy surface and thus so does the equilibrium geometry.

aug-cc-pV5Z – quintuple-zeta basis, 5 functions to describe atomic orbitals in the valence shellICMRCI – internally contracted multireference configuration interaction

Data fromJonathon Tennyson

Complete basis set


Chemistry

There are a large number of people who calculate important points on PESs – transition states and equilibrium structures – to determine the energetics of reactions.Optimizing to a transition state finds one imaginary frequency (negative force constant, corresponding to the barrier).

TS

eqeq


Chemistry

Complicated reactions such as propargyl radical recombination to make benzene in flames consist of many transition states and minima.


ChemistryYou can go crazy.


Chemistry


How to be chemically accurate?

For chemistry, we would like energies to be accurate to within about 4 kJ/mol. So we need to use a very good method, but it would be very expensive to do everything with configuration interaction at the complete basis set limit.

Geometry optimizations and frequency calculations (for zero point energies) take a lot of effort, and cannot be done with high levels of theory.

We could calculate geometries at one level, and energies at another, e.g. CCSD/6-31G(d)//B3LYP/6-31G(d). Here we get the density function theory geometry and then use a so-called coupled-cluster calculation to get the energy.

But, smart people (Curtiss, Pople) have developed combinations of methods which end up being chemically accurate, with more modest cost.


Model Chemistries

The Gaussian-1 method, for instance


Model Chemistries


Model Chemistries: G1, G21989 1991


G3 Theory 1998

The Nobel Prize in Chemistry 1998 was divided equally between Walter Kohn "for his development of the density-functional theory" and John A. Pople "for his development of computational methods in quantum chemistry".

J. Chem. Phys. 109, 7764 (1998); Gaussian-3 (G3) theory for molecules containing first and second-row atoms

Larry A. Curtiss, Krishnan Raghavachari, Paul C. Redfern, Vitaly Rassolov, and John A. Pople

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1998/kohn.html

http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1998/pople.html

©2013, jordan, schmidt & kable lecture 16 lecture 16 molecular structure and thermochemistry...

Documents

schmidt kablelecture

potential energy curve

electronic states cross

ground states

chemical accuracy

oppenheimer breakdown

reaction barrier

equilibrium geometries