Basic fundamentals of theoretical, quantum and computational chemistry. The methods and approaches helps in predicting the electronic structure properties as well as other spectral data.

1. Introduction to
Computational chemistry
and its tools
Girinath G Pillai, PhD
@giribio

3. ● Materials might contain pictures / videos / codes / materials from public resources
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● We declare no conflict of interest and does not have any connection with their
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Contents
3

4. “Deepest part of theoretical chemistry must end
up in quantum mechanics”
— Richard P. Feynman
4

5. Computational & materials modeling
Accelerate research, reduce costs & environmental impact
● Reduce experimental search space
● Analyze structure-property-reactivity
Models: physics & empiricism
● Accuracy?
Synergy experiment-calculations
● Ask relevant questions
● Limitations model
● Constraints experiments
Why bother with Simulations?
5

6. Pauli's exclusion principle turned 97
6

7. Now we have large computers and faster PCs
Quantum Chemistry
7
The general theory of quantum mechanics
is now complete... The underlying physical
laws necessary for the mathematical theory
of a large part of physics and the whole of
chemistry are thus completely known
– Paul Dirac, 1929.
Right: QM is the foundation of Chemistry
Wrong: Not so fast - complexities necessitate approximations

8. 8
Hatree
1687
Fock
1687
Heisenberg
1932

9. Nobel Prize in Chemistry 1998
9
John A. Pople
"for his development of computational
methods in quantum chemistry"
Walter Kohn
"for his development of the density
functional theory”
DFT

10. Nobel Prize in Chemistry 2013
10
Martin Karplus Michael Levitt Arieh Warshel
"for the development of multiscale models for complex chemical systems"

11. Need of Computational Simulations
11

12. Theoretical Foundation
12
Isaac Newton
1687
James Clark Maxwell
1864
Ludwig Boltzmann
1871
Josiah Willard Gibbs
1876
Erwin Schrödinger
1926
Classical Mechanics Electrodynamics Statistical Mechanics Quantum Mechanics

13. A branch of chemistry, that uses equations encapsulating the behavior of matter on
an atomistic scale and uses computers to solve these equations
To calculate structures and properties of molecules, gases, liquids and solids
To explain or predict chemical phenomena.
Computational Chemistry?
13

14. ● Molecular mechanics
● Semiempirical molecular orbital methods
● Ab initio molecular orbital methods
● Density functional method
● Quantum Monte Carlo method
● …
Yields Energy, Structure, and Properties
Comp. Chem. Methods
14

15. Including:
● Electron dynamics
● Time independent ab initio
calculations
● Semi-empirical calculations
● Classical molecular dynamics
● Embedded models
● Coarse grained models
Comp. Chem. is...
15
Not Including:
● Quantum chromodynamics
● Calculations on Jellium
● Continuum models
● Computational fluid dynamics
● Data mining
● Rule based derivations

16. ● Quantum Mechanical
○ via Schrodinger equation is also called Quantum Chemistry
● Molecular Mechanical
○ via Newton’s Law also called Molecular Dynamics
● Empirical/Statistical
○ via QSPR
Applications of Comp. Chem.
16

17. ● Simplest type of calculation
■ Used when systems are very large and approaches that are more accurate
become to costly (in time and memory)
● Does not use any quantum mechanics instead uses parameters derived from
experimental or ab initio data
■ Uses information like bond stretching, bond bending, torsions, electrostatic
interactions, van der Waals forces and hydrogen bonding to predict the
energetics of a system
■ The energy associated with a certain type of bond is applied throughout the
molecule. This leads to a great simplification of the equation
● It should be clarified that the energies obtained from molecular mechanics
do not have any physical meaning, but instead describe the difference
between varying conformations (type of isomer). Molecular mechanics can
supply results in heat of formation if the zero of energy is taken into account.
Molecular Mechanics
17
Courtesy of Shalayna Lair, University of Texas at El Paso

18. ● AMBER, CHARMM, NAMD
● VMD - Visual Molecular Dynamics
● MOLDY - Free MD program
● GROMACS Molecular Dynamics on Parallel Computers
● GROMOS Dynamic Modelling of Molecular Systems
● MacroModel - Molecular Modelling
● MSI/Biosym Molecular Modelling Software
● NAMD - Scalable Molecular Dynamics
● TINKER package for molecular mechanics and dynamics
● SYBYL - software from Tripos
● X-PLOR- MM program free for Academics
● DNAtools-Web tools to analyze DNA
MM Tools
18

19. ● Semiempirical methods use experimental data to parameterize equation
● Like the ab initio methods, a Hamiltonian and wave function are used
■ most of the equation is approximated or eliminated
● Less accurate than ab initio methods but also much faster
● The equations are parameterized to reproduce specific results, usually the
geometry and heat of formation, but these methods can be used to find other
data.
Semiempirical
19
Courtesy of Shalayna Lair, University of Texas at El Paso

20. ● Single determinant, the Hartree-Fock method.
● Given the approximate wavefunction PSI, and the total energy of the system
from the wavefunction, the solution point is reached when the following
variational process comes to the point where all energy derivatives with
respect to the variables (LCAO coefficients) vanish.
Hartree–Fock Method
20

21. ● “ab initio” – Latin, means “from the beginning” or “from first principles.”
● No experimental input is used and calculations are based on fundamental laws
of physics.
● Various levels of ab initio calculations (jargons):
○ Hartree-Fock Self-Consistent Field (HF-SCF)
■ simplest ab initio MO calculation
■ electron correlation is not taken into consideration.
○ Configuration Interaction (CI)
○ Coupled-Cluster (CC)
○ The Møller-Plesset Perturbation Theory (MP)
○ Density Functional Theory (DFT)
ab initio Methods
21
Courtesy of Shalayna Lair, University of Texas at El Paso

22. ab initio Methods
22

23. Areas where Comp. Chem. applied
23
Quantum
Chemistry
Main Group
Thermochemistry
Non Covalent
Interactions
Themochemical
Kinetics
Transition Metal
Chemistry
Long Charge
Transfer
Spectroscopy
Courtesy of Donald G Truhlar

24. To solve the Schrödinger equation approximately, assumptions
are made to simplify the equation:
● Born-Oppenheimer approximation allows separate treatment of nuclei and
electrons. (ma
>> me
)
● Hartree-Fock independent electron approximation allows each electron to be
considered as being affected by the sum (field) of all other electrons.
● LCAO Approximation represents molecular orbitals as linear combinations of
atomic orbitals (basis functions).
Approximations
24
Courtesy of Hai Lin

25. LDA describes only the local-point
effects of the density,
GGA the density gradient at the given
point is added, and
meta-GGA the local kinetic energy and
density are used as the arguments.
Methods of Approximations
25
Iurii Kim, Alto University, 2015

26. 26

27. Which one to choose?
● LDA: Good atomic coordinates, poor energetics, poor band gaps.
● GGA/PBE: Fair atomic coordinates, good energietics for local interactions,
poor band gaps.
● vdW/vdW-DF: Fair atomic coordinates for non-metals, poor for metals,
good non-local energetics, poor band gaps.
● Hybrids/HSE: Good atomic coordinates, good energies, fair band gaps.
Slower.
27

28. ● Choose start coefficients for MO’s
● Construct Fock Matrix with coefficients
● Solve Hartree-Fock-Roothaan equations
● Repeat 2 and 3 until ingoing and outgoing coefficients are the same
○ To solve the Hartree-Fock-Roothaan equation, self-consistent-field procedure is
employed, where one starts from a trial solution, builds a Fock matrix, and then
diagonizes it to find the eigen functions to start the next iteration. The process
keeps going on until the energy and/or density differences between two steps are
less than certain criteria.
Self Consistent Field - SCF
28

29. ● atomic orbitals, are called basis functions
● usually centered on atoms
● can be more general and more flexible than atomic orbital functions
● larger number of well chosen basis functions yields more accurate
approximations to the molecular orbitals
Slater-type orbitals (STO)
Minimal STO-nG
Gaussian-type orbitals (GTO)
Split Valence: 3-21G,4-31G, 6-31G
LCAO > Basis Functions
29

30. Polarization: Add AO with higher angular momentum (L) to give more flexibility
Example: TZVPP, 3-21G*, 6-31G*, 6-31G**, etc.
Diffusion: Add AO with very small exponents for systems with very diffuse electron
densities such as anions or excited states
Example: TZVPD, 6-31+G*, G**
Polarization/Diffusion
30

31. ● a family of basis sets of increasing size
● can be used to extrapolate to the basis set limit
● cc-pVDZ – DZ with d’s on heavy atoms, p’s on H
● cc-pVTZ – triple split valence, with 2 sets of d’s and one set of f’s on heavy
atoms, 2 sets of p’s and 1 set of d’s on hydrogen
● cc-pVQZ, cc-pV5Z, cc-pV6Z
● can also be augmented with diffuse functions (aug-cc-pVXZ)
Correlation Consistent bf
31

32. ● core orbitals do not change much during chemical interactions
● valence orbitals feel the electrostatic potential of the nuclei and of the core
electrons
● can construct a pseudopotential to replace the electrostatic potential of the
nuclei and of the core electrons
● reduces the size of the basis set needed to represent the atom (but
introduces additional approximations)
● for heavy elements, pseudopotentials can also include of relativistic effects
that otherwise would be costly to treat
●
Pseudopotentials, Effective Core
32

33. ● 1926: Old DFT -- Thomas-Fermi theory and extensions.
● 50’s-60’s: Slater and co-workers develop Xα as crude KS-LDA.
● 1965: Modern DFT begins with Kohn-Sham equations. By introducing
orbitals, get 99% of the kinetic energy right, get accurate n(r), and
only need to approximate a small contribution, EXC[n].
● 1965: KS also suggested local density approximation (LDA) and
gradient expansion approximation.
● 1993: More modern functionals (GGA’s and hybrids) shown to be
usefully accurate for thermochemistry
● 1995-: TDDFT & hybrid DFT methods
● 1998: Kohn and Pople win Nobel prize in chemistry
● 2000-: DFT with dispersion/long-range corrected DFT
● 2010: DFT in materials science, geology, soil science, astrophysics,
protein folding,...
Density Functional Theory
33

34. Impact of DFT
34

35. HK 1964 Hohenberg, Kohn, Phys. Rev. 136, B864 (1964)
KS 1965 Kohn, Sham, Phys. Rev. 140, A1133 (1965)
CA 1980 Ceperley, Alder, Phys. Rev. Lett. 45, 566 (1980)
PZ 1981 Perdew, Zunger, Phys. Rev. B 23, 5048 (1981)
PBE 1996 Perdew, Burke, Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)
Impact of DFT
35

36. ● Transferability
○ We can use the same codes/methods for very different materials
● •Simplicity
○ The Kohn-Sham equations are conceptually very similar to the Schr¨odinger
equation for a single electron in an external potential
● Reliability
○ Often we can predict materials properties with high accuracy, sometimes even
before experiments
● Software sharing
○ The development of DFT has become a global enterprise, e.g. open source and
collaborative software development
● Robust platform
○ Often the shortcomings of DFT can be cured by using more sophisticated
approaches, which still use DFT as their starting point
Why DFT so popular?
36

37. 1964 Hohenberg–Kohn theorem and Kohn–Sham formulation
1972 Relativistic extension of density functional theory
1980 Local density approximation for exchange and correlation
1984 Time-dependent density functional theory
1985 First-principles molecular dynamics
1986 Quasiparticle corrections for insulators
1987 Density functional perturbation theory
1988 Towards quantum chemistry accuracy
1991 Hubbard-corrected density functional theory
1996 The generalized gradient approximation
Exponential rate of progress in the past two decades
37

38. Methods & Properties
38

39. Hybrid : B3LYP (1993) - Becke-3 parameter Lee-Yand-Parr
GGA: BLYP (1988)
But others are also used like
M06
BP86
PBE
etc.,
B3LYP is popular
39
Sousa Fernandes Ramos, JPCA 2007

40. Is there a particular category of computations that is of most interest?
– Structure:
● Geometry optimizations based on model chemistry
● Comparison of computational results to experimental results
● Transition state geometries
– Property:
● Electrical, optical, magnetic, etc
● Determination of spectra, from NMR to X-Ray
● Calculation of quantum descriptors
– Quantitative structure-property relationship (QSPR)
– (Re)activity:
• Reaction mechanisms in chemistry and biochemistry
• QSAR-types of problems
– Quantitative structure-activity relationship (QSAR) is the process by which
chemical structure is quantitatively correlated with a well defined process
Which system for which method?
40

41. Ab initio MO Methods
CCSD(T) quantitative (1~2 kcal/mol) but expensive ~N6
MP2 semi-quantitative and doable ~N4
HF qualitative ~N2-3
DFT Methods
DFT semi-quantitative and cheap ~N2-3
Semi-empirical MO Methods
AM1, PM3, MNDO semi-qualitative ~N2-3
Molecular Mechanics Force Field
MM3, Amber, Charmm semi-qualitative (no bond-breaking) ~N1-2
Methods in Comp. Chemistry
41
Quality Size
Dependence

42. Size vs Accuracy
42

43. Limits of Comp. Chem.
43

44. Cost vs Accuracy
44
Method ~ max atoms
~ relative
cost
scaling
Typical
Accuracy*
Classical force field
(UFF, Amber, … )
1,000,000 0.0005 N
1 <20 kcal/mol
Reactive force field 500,000 0.001 N
1 <15 kcal/mol
Semi-empirical methods
(e.g. AM1, PM7)
5,000 1 N
1~2 <10 kcal/mol
DFTB 5,000 1 N
1~2 <10 kcal/mol
DFT 500 500 N
3~4 <5 kcal/mol
MP2 100 2000 N
5 <5 kcal/mol
CCSD(T)/cc-pVTZ 30 100000 N
6 ~1 kcal/mol

45. – No edge effects
– Larger models
– Plane wave basis set
– IR and Raman freq.
– Specific calculations: TSs, crossing
points
– Pure DFT
– Heavy calcs for Hybrid methods
& localized basis sets
Periodic vs Finite!
45
– Hybrid methods: B3LYP
– Localized basis sets
– IR and Raman intensities
– Specific calculations: TSs, crossing
points
– Smaller model
– Edge effects
– No coverage effect

46. QM/MM - Hybrid
Eg. biosystems (protein-ligand, enzyme-substrate)
Eg. zeolites
Merits
Large Systems
Very versatile
Difficulties
○ Long calculation times
○ Difficult description border zones
○ between levels
○ MM Potential not always available
Approx. large systems
46

47. >These questions should be answered
● What do you want to know?
● How accurate does the prediction need to be?
● How much time can be devoted to the problem?
● What approximations are being made?
>The answers to these questions will determine the type of calculation, method and
basis set to be used
● Model Chemistry
>If good energy is the goal >> use extrapolation procedures to achieve `chemical
accuracy’: G1/2/3, W1/2/3, PCI-80… models
● DFT is always a good start for chemical systems
Start Comp. Chem. project?
47

48. Everything starts with an energy expression
Calculations either minimize to obtain:
● the ground state
● equilibrium geometries
Or differentiate to obtain properties:
● Infra-red spectra
● NMR spectra
● Polarizabilities
Or add constraints to
● Optimize reaction pathways (NEB, string method, ParaReal)
The choice of the energy expression determines the achievable accuracy
Start with...
48

49. Issues for ML:
● arbitrary size
● arbitrary order
Ideal features:
● general
● compact
● unique
● invariant *
● smooth
● fast
010110101010001011100100010001111110
ML methods need a computer-friendly way to input the atomistic system:
easy for us
easy for CPU
* invariants are determined by the physics of the quantity to predict from the descriptor!
49
Descriptors for Chemistry

50. 010110101010001011100100010001111110
ML methods need a computer-friendly way to input the atomistic system:
Global
Descriptor
110100011110000110010111111110
110100011110001011100001111110
010110101010001011100001111110
Local/Atomic
Descriptor
50
Descriptors for Chemistry

51. 1. .xyz
2. .cif
3. .mol
4. .mol2
5. .sd / sdf
6. .pdb
7. .skc/.cdx/.mrv/…
8. .smi CCCC
File Formats
51

52. OpenBabel
● Multiple chemical file formats (+ options) and utility formats
● 2D coordinate generation and depiction (PNG and SVG)
● 3D coordinate generation, forcefield
minimisation, conformer generation
● Binary fingerprints (path-based, substructure
based) and associated “fast search” database
● Bond perception, aromaticity detection and
atomtyping
● Canonical labelling, automorphisms, alignment
● Plugin architecture
● Several command-line applications, but also a software library
Format Convertor
52

53. Software Requirements
● Comprehensive functionality
● Easy to use
● Computationally efficient
● Validated
● Robust
● Well documented
● Fully supported over decades on changing hardware and OS
● Extensible
● Interoperability with other software components and platforms
● Compliance with standards
53

54. ● ORCA, NWChem, GAMESS, Psi4
● Turbomole, ADF, Gaussian, MolPro, Q-Chem, Molcas, DMol3, Jaguar
● ABINIT, Seista, CRYSTAL
● VASP, Quantum ESPRESSO, BAND, ONETEP, CASTEP
Quantum Chemistry Softs.
54

55. Molden
Jmol
GabEdit
NGLView
ECCE
Arguslab
VMD
VegaZZ
DeepView
Discovery Studio Visualizer
MolView and Molview Lite - Macintosh
Editors and Visualizers
55
Materials Studio Visualizer
Crystal Maker
VMD
VESTA
AMS GUI
ModelView
MOLDRAW (Molecules and crystals)
Molekel (Molecules and crystals)
PBCs
Molecules

56. Adapt from
others
Learn but apply with your own ideas
and creativity
56

57. Until you
try yourself and
train others
you cannot be
an expert
57

58. CREDITS: This presentation uses icons by Flaticon,
and infographics & images by Freepik.
Thanks!
Do you have any questions?
@giribio
Please keep this slide for attribution.
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