Introduction to Quantum Chemistry Simulations with ORCA (PDF)

Texas A&M HPRC Short Course Series Introduction to Quantum Chemistry Simulations with ORCA Xin Yang Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Outline 10:00 -10:20 Intro to Computational Chemistry 10:20 -...

Texas A&M HPRC Short Course Series Introduction to Quantum Chemistry Simulations with ORCA Xin Yang Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Outline 10:00 -10:20 Intro to Computational Chemistry 10:20 -10:35 Hands-on Session 1 –Set up an ORCA calculation 10:35-11:10 Basics of Quantum Mechanical Simulation 11:10-11:45 Hand-on Session 2 – Geometry optimization and frequency calc. 11:45-12:00 Calculations of Molecular Properties 12:00-12:15 Hands-on session 3 – Prediction of UV/Vis Spectra 12:15-12:30 Wrap-up Lecture Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Microscopic ó Macroscopic Time Grids >min Continuum s Segments (FEA, CFD) µs Mesoscale ns Atoms ps Molecular Electrons Dynamics fs F=ma Quantum Mechanics HY=EY Ångstroms nm µm mm m Distance Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ What is computational chemistry? Computational Chemistry: Use mathematical approximations and computer programs to obtain results relative to chemical problems. Quantum Mechanical i.e., via Schrödinger Equation also called Quantum Chemistry Molecular Mechanical i.e., via Newton’s law F=ma also called Molecular Dynamics Empirical/Statistical/Machine Learning e.g., QSAR, etc., widely used in clinical and medicinal chemistry also called Cheminformatics Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Why do we need computational chemistry? Assist experimental chemists to bypass tedious, time consuming, costly, and sometimes dangerous experiments EXAMPLE: Drug design Investigate molecules that are too unstable to be studied experimentally, analyze quantities (such as atomic charges) that are not experimentally observable, and rectify incorrect experimental assignments EXAMPLE: methylene radical (:CH2) , linear or bent? Calculate certain quantities with more accuracy than can be determined experimentally and improve one’s general understanding of chemical phenomena. EXAMPLE: Solubility, Enthalpies formation, Reaction Mechanisms Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Computational Quantum Chemistry Solve the Schrödinger equation for molecular systems HY = EY Ĥ Hamiltonian Operator y Wavefunction (eigenfunction) E Energy of the system (eigenvalue) What is the typical size of system do we deal with? Assuming typical computing setup (number of CPUs, memory, disk space, etc.) Ab initio method: between 1 and ~50 atoms depending on the level of theory DFT method: ~100 atoms Semi-empirical method: larger than DFT (approximate solution, highly parameterized) Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Quantum Mechanical Methods ab initio methods Hartree-Fock Methods: HF, RHF, URH Post-Hartree Fock Methods: MPn, CI, CC, QCI Multireference Methods: CASSCF (NEVPT2, CASPT2) Applicable to any system, in principle Computationally expensive Typically used for small system ( normally < 50 atoms ) Scaling: Nn n=2, 3, 4, 5, 6, … Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Quantum Mechanical Methods Density Functional Theory (DFT) Total energy of a system depends only on the electron density 1 𝜌(𝐫#)𝜌(𝐫$) ) 𝐸! 𝜌 = $𝜌 𝐫 𝑣 𝐫 𝑑𝐫 + 𝑇" 𝜌 + - 𝑑𝐫#𝑑𝐫$ + 𝐸%& 𝜌 2 𝑟#$ Single determinant method Includes electron correlation with little cost compared to ab initio methods Not as dependent on the quality of the basis set as wave function methods Exact functional is not known, results may vary with the choice functional Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Reaction Mechanism Calculations Geometry optimization Thermochemistry Transition state search Intrinsic reaction coordinate To understand the regioselectivity of polymer initiation step. https://doi.org/10.1021/jacs.0c05610 Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  IR Spectra DFT Calculation Calculated by default for frequency calculations in ORCA and most QM codes. Only fundamental transitions are predicted, so no overtones and combination bands are included. Correct frequencies with a scaling factor Experiment By default, only thin lines corresponding to each frequency are printed. In order to make your predicted spectra look more like an experimental one, some line broadening is needed. https://webbook.nist.gov/cgi/cbook.cgi?ID=C7732185 Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ UV/Vis Spectra via TD-DFT TD-DFT Calculation for 1E STATE 1: E= 0.112459 au 3.060 eV 24682.0 cm**-1 50a -> 55a : 0.056581 (c= 0.23786860) 54a -> 55a : 0.913932 (c= -0.95599797) 54a -> 59a : 0.010570 (c= 0.10281285) State 1 is composed of about 91% a HOMO to LUMO transition, from orbital 54 to orbital 55 (the "a" there means alpha orbital). TD-DFT predicted Spectra HOMO LUMO exp. 490 nm exp. 404 nm cal. 503 nm orb #55 orb #56 cal. 405 nm !!! Avogadro counts orbitals starting from 1, but ORCA starts counting from 0. So orbital 54 in ORCA will be orbital 55 in Avogadro, and ABS so on. https://www.orcasoftware.de/tutorials/spec/UVVis.html J. Am. Chem. Soc. 2009, 131, 43, 15594–15595 Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  NMR Spectra ! NMR shifts are quite dependent on the magnetic shielding constants (or the chemical shifts δ) conformer you choose. A conformer search or spin–spin coupling constants even a Boltzmann weighting might be necessary! Generate a library of conformers (Conformational search, eg. MacroModel) Determine optimal geometries, free energies, chemical shift δ, and J for each conformer (DFT, eg. ORCA) Calculate Boltzmann-weighted chemical shifts and coupling constant nmrdb Nat Protoc 9, 643–660 (2014). Angew.Chem. Int. Ed. 56, 14763 –14769 (2017). Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ QM Simulation Software Name Description Price* ABINIT QM (Molecular and Periodic Systems) Free ADF QM (Slater orbitals) $ AMPAC QM (Semi-empirical) $ GAMESS-US QM Free Gaussian QM $ MOLPRO QM (specializing in high-level calculations) $$ NBO Wavefunction analysis program $ NWChem QM Free ORCA QM specializing in spectroscopic properties Free Quantum ESPRESSO QM solid state and surfaces Free SIESTA QM specializing in electron transport and Solids Free VASP QM specializing in QMD and ultra-soft ECPs $$ * Academic Pricing Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  ORCA ORCA is an ab initio, DFT, and semi-empirical SCF-MO package developed by Frank Neese et al. at the Max Planck Institut für Kohlenforschung. ORCA Forum ORCA Tutorial Robust Free and open-source Cross platforms Runs parallel Easy to install Active in development … Runs completely from command line Needs third-party visualization tools Neese, F. (2012) The ORCA program system, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2, 73-78. Neese, F. (2017) Software update: the ORCA program system, version 4.0, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 8, e1327. Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Avogadro http://avogadro.cc/ Avogadro is a free, open source molecular editor and visualization tool, designed for use on Mac, Windows, and Linux in computational chemistry, molecular modeling, bioinformatics, materials science, and related areas. It offers flexible high quality rendering and a powerful plugin architecture. Figures from http://avogadro.cc/ Cross-Platform Free, Open Source International Intuitive Fast Extensible Flexible Marcus D Hanwell, Donald E Curtis, David C Lonie, Tim Vandermeersch, Eva Zurek and Geoffrey R Hutchison; “Avogadro: An advanced semantic chemical editor, visualization, and analysis platform” Journal of Cheminformatics 2012, 4:17. Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Hands-on Session #1 – 15 minutes In this hands-on session, you will run an ORCA calculation using pre-prepared input. Login to the Vidi Portal: https://vidiportal.chem.tamu.edu/ Open a terminal and load the appropriate modules Take a look at the format of the h2.inp file Use the command line to submit an orca job Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Hands-on Session #1 – 15 minutes Avogadro Draw tool, Navigation tool, Measure tool, Selection tool - left click Delete – right click Draw a bond – left click and drag Change bond lengths, angles, torsions - View Menu > Properties Insert Fragment – Build Menu > Insert https://avogadro.cc/ Quick Optimization – Extension Menu > Optimize Geometry Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Getting Started with QM simulations What do we need? ORCA Sample Input Atomic coordinates ! B3LYP Def2-SVP OPT FREQ Symmetry (Optional) Charge *xyz 0 1 O -5.47612 3.94470 0.00000 Multiplicity H -4.50612 3.94470 0.00000 H -5.79945 3.48041 -0.78791 * Level of Theory (Methods) Basis Set Job Type: single point, geometry optimization, frequency calculation Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Atomic Coordinates All atoms including hydrogens ORCA Simple Input: XYZ coordinates in Å cartesian coordinates *xyz 0 1 internal coordinates O -5.47612 3.94470 0.00000 H -4.50612 3.94470 0.00000 z-matrix H -5.79945 3.48041 -0.78791 Internal redundant coordinates * File formats:.xyz,.mol,.pdb, etc. ORCA Simple Input: Z-matrix format C2H6 *gzmt 0 1 D3d O Charge = 0 H 1 0.97000 Multiplicity = 1 H 1 0.97000 2 109.47100 * Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Atomic Coordinates Atomic (nuclear) coordinates are required for all atomistic calculations. A reasonably good starting geometry is required for electronic structure calculations. Bad starting A reasonable starting structure! geometry is required for electronic Will most likely structure calculations. fail with an SCF convergence failure or possibly optimize Good starting to an excited state. structure! Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Charge, Spin, and Multiplicity Charge (overall charge of the molecular system) Spin State – How many unpaired electrons? Spin Multiplicity = 2S+1 where S is the total Spin S=Sms ms = ½ spin up, alpha ms = -½ spin down, beta Number of Spin Quantum Spin unpaired e- Multiplicity State 0 S=0 1 Singlet 1 S=1/2 2 Doublet 2 S=1 3 Triplet 3 S=3/2 4 Quartet 4 S=2 5 Quintet Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Charge, Spin, and Multiplicity EXAMPLE 1: H2O neutral, charge = 0 no unpaired e-, S=0, Multiplicity = 2S+1 =1 2p *xyz 0 1 O -5.47612 3.94470 0.00000 H -4.50612 3.94470 0.00000 H -5.79945 3.48041 -0.78791 * EXAMPLE 2: O2 2s neutral, charge = 0 2 unpaired e-, S= ½ + ½ = 1, 2S+1 =3 Triplet O O-O O *int 0 3 O Molecular Oxygen Molecular Orbital Diagram O 1 1.31600 Triplet is the Ground State * adapted from https://commons.wikimedia.org/wiki/File:MO_diagram_dioxygen.png Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Getting Started with QM simulations Choose a level of theory The level of theory determines the Hamiltonian (H) used to solve the Schrödinger equation HΨ=EΨ HF, MP2, MP3, DFT (B3LYP, etc.), CCSD, etc Choose a basis Set Basis sets is a set of coefficients and exponents used to describe the atomic orbitals that will be using to describe the wave function 6-31G(d), def2-TZVP, Effective Core Potential (ECP):SDD, LANL2DZ Choose a job type Single point (default), geometry optimization, frequency calculations, etc. Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Quantum Mechanics – Many e- Hamiltonian M N N M N N M M ˆ 1 1 Z 1 ZA ZB H = −∑ ∇A − ∑ ∇i − ∑ ∑ 2 2 A + ∑∑ + ∑ ∑ A =1 2M A i=1 2 i=1 A =1 riA i=1 j >i rij A =1 B >A rAB Hˆ = Tˆn + Tˆe + Vne + Vee + Vnn Tˆn = Kinetic energy operator for the nuclei Tˆ = Kinetic energy operator for the electrons e Vne = Coulombic attraction between the elecrons and nuclei Vee = Coulombic repulsion between the elecrons Vnn = Coulombic repulsion between the nuclei Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Quantum Mechanics Hˆ = Tˆn + Tˆe + Vne + Vee + Vnn Hˆ = Hˆ n + Hˆ e = Hˆ n + Hˆ o + Hˆ 1 = Tˆn + Vnn + Tˆe + Vne + (Vee ) ( ) ( ) ψ o = Slater Determinant φ1 (1) φ1 (1) …. φ N / 2 (1) φ N/2 (1) 1 φ1 (2) φ1 (2) …. φ N/2 (2) φ N/2 (2) = …. …. …. …. N! φ1 ( N ) φ1 ( N ) …. φ N/2 ( N ) φ N/2 ( N ) Satisfies indistinguishability of the electrons and antisymmetry requirement of the wavefunction. Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Hartree-Fock Theory N N N N ˆ 1 Z 1 H e = − ∑ ∇i − ∑ + ∑ ∑ 2 2 i=1 i=1 ri i=1 j >i rij Hˆ e = Tˆe + Vˆne + Vˆee 2e- interactions Sum of 1e- interactions N = number of electrons Tˆe = Kinetic energy operator for the electrons Vˆ = Coulombic attraction between the elecrons and the nuclei ne Vˆee = Coulombic repulsion between the elecrons Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Hartree-Fock Theory Variational (EHF≥E1) Size-Extensive (EA.. A=EA+EA) Size-extensive: 2EA = EA.. A Where, EA is the energy of molecule A and EA.. A is the energy of two molecules of A separated by a large distance (i.e. non-interacting) Size-intensive: 2EA ≠ EA.. A Neglects instantaneous e- correlation Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/ Electron Correlation Electron Correlation – the motion of electrons are correlated Coulomb hole – the probability of finding an electron of opposite spin near another electron is small Fermi hole – the probability of finding an electron with the same spin near another electron is small Hartree-Fock theory included electron correlation of electrons of the same spin (Fermi Hole) but does not include electron correlation of electrons of opposite spin. How to include electron correlation for electrons of the opposite spin (instantaneous e- correlation)? Post-HF: Møller-Plesset Perturbation theory (MPx (x=2, 3, 4, …)), Configuration Interaction (CI), Coupled-Cluster (CC), …. Density Functional Theory Texas A&M University HPRC https://hprc.tamu.edu LMS https://lms.hprc.tamu.edu/  Ab initio Summary HF