Basics of Quantum and Computational Chemistry
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The document provides an overview of computational chemistry and its tools, highlighting its significance in accelerating research and reducing environmental impact through modeling. It discusses various computational methods, including molecular mechanics, semiempirical techniques, and ab initio calculations, along with their applications and limitations. Additionally, it emphasizes the role of quantum mechanics and the importance of modern advances like density functional theory (DFT) in the field.
![● 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
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Basics of Quantum and Computational Chemistry
- 1. Introduction to Computational chemistry and its tools Girinath G Pillai, PhD @giribio
- 3. ● Materials might contain pictures / videos / codes / materials from public resources with ‘right to reuse’ rights and the copyrights and ownerships goes to the respective authors. ● We declare no conflict of interest and does not have any connection with their employer, employee or others. ● Slides are shared via Slideshare - https://www.slideshare.net/giribio 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
- 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
- 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
- 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
- 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. 58