Baran Lab Steven McKerrall Modern Computational Organic Chemistry Group Meeting Overview: Computational Chemists Featured in this Talk (not exaustive!) Classical Computational Chemistry 1. History of computational chemistry 2. Introduction to chemical calulations (for organic chemists) – quantum mechanics, a review Quantum – Hartree-Fock theory Chemical – basis functions/basis sets Theory – post-Hartree-Fock methods – density-functional theory – computational methods, an overview 3. Computing physical properties – aromaticity – spectral properties: IR, NMR, CD How to employ Douglas Hartree Vladimir Fock Walter Kohn John Pople (1897–1958) (1898–1974) (UCSD, UCSB) (1925-2004) 4. Analyzing organic reactions computational methods – general concepts: transition state theory Contemporary Computational Organic Chemistry – dyotropic reactions – cationic rearrangements in terpene biosynthesis 5. Quantum tunneling effects – light-atom tunneling – heavy-atom tunneling – tunneling in enzyme catalysis Unusual mechanisms in 6. Deviations from TST: potential energy surface bifurcations organic – valley-ridge inflections (VRIs) chemistry – bifurcations where you'd least expect them – selectivity in bifurcated PESs Don Truhlar Paul v. R. Schleyer Ken Houk (UCLA) Henry F. Schaefer III (Minnesota) 7. Deviations from TST: dynamic effects in organic reactions 922 (UGA) 1019 1209 (UGA) – computational dynamics 1428 – non-statistical dynamics in organic reactions – dynamic effects in terpene biosynthesis Significant References: Computational Organic Chemistry (2007), Steven M. Bachrach Essentials of Computational Chemistry (2002), Christopher J. Cramer Chris Cramer Encyclopedia of Computational Chemistry (1998), Paul von Ragué Schleyer Daniel Singleton Peter Schreiner Dean Tantillo (Minnesota) (Texas A&M) (Giessen) (UC Davis) 366 308 167 1 Baran Lab Steven McKerrall Modern Computational Organic Chemistry Group Meeting 1. History of Computational Chemistry Computational Chemistry is the use of computer simulation to predict, understand, or explain chemical reactivity. Number of citations per year to "DFT" (unfilled) and "Gaussian" (filled) Nobel Prizes in Computational Chemistry: -Walter Kohn (1998): "for his development of density-functional theory" from Computational Organic Chemistry -John Pople (1998): "for his development of computational methods in quantum chemistry" -Martin Karplus, Michael Levitt, and Arieh Warshel (2013): "for the development of multiscale models for complex chemical systems" 5 of the top 10 most cited papers of all time in JACS are computational: 1. Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model (7854) Moore's Law: The number of transistors 2. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and on integrated circuits doubles Organic Molecules (3338) approximately every two years. 3. Development and Testing of the OPLS All-Atom Force Field on Conformational The ever-increasing computing power of Energetics and Properties of Organic Liquids (3011) modern computers drives the extension 6. Nucleus-Independent Chemical Shifts: A Simple and Efficient Aromaticity Probe of computational chemistry to more (2207) complicated systems with more sophisticated levels of theory 8. A new force field for molecular mechanical simulation of nucleic acids and proteins (1490) A Brief History: 1925 – Warner Heisenberg, Max Born, and Pascal Jordan develop matrix mechanics – Erwin Schrödinger invents wave mechanics and non-relativistic Schrödinger equation – Walter Heitler and Fritz London publish first calculations on chemical bonding 1927 – Douglas Hartree publishes self–consistent field method 1930 – Vladimir Fock formulates Hartree–Fock theory Much of modern computational 1947 – ENIAC is the first general–purpose computer to be built chemisry is performed on linux 1950 – Clemens Roothaan publishes LCAO theory clusters where multiple processors can 1951 – UNIVAC is the first commercial general–purpose computer be utilized and many calculations can be run in parallel 1955 – First ab initio calculation on 'large' molecule, N2 – Transistors replace vacuum tubes in computers 1964 – Pierre Hohenberg and Walter Kohn introduce density–functional theory 1970 – John Pople introduces Gaussian (software) 1971 – First commercially available microprocessor (Intel 4004) 2 Baran Lab Steven McKerrall Modern Computational Organic Chemistry Group Meeting 2. Introduction to chemical calculations With the one electron wavefunction assumption the total Quantum Mechanics, a Review electronic energy can be described as the sum of electronic energies Ei. Which arise from the Hartree equation: Quantum chemical calculations entail solution of the time-independent Schrödinger equation eff (K + Ve-n + Vi )φi = Eiφi HΨ(R1...Rn,r1...rn) = EΨ(R1...Rn,r1...rn) – K is the kinetic energy operator for electrons – H is the Hamiltonian operator (which describes potential and kinetic energy of the – V is the potential energy operator from electron nucleus attraction molecule) – V eff is the effective field of all other electrons – Ψ(x) is the wavefunction for nuclei and electrons (a function of nuclear positions R and i electron positions r) – E is the energy associated with the wavefunction The probability density of a wavefunction is given by its square (technically complex Self-consistent field: solving for a set of functions φi is still problematic because the conjugate), 2 eff Ψ effective field Vi is dependent on the wavefunctions. To solve this problem an iterative Hartree-Fock Theory procedure is used where: 1. a set of functions, (φ1...φn) is guessed eff There are very few scenarios for which an analytic solution fo the Schrödinger equation exists. 2. to produce a potential Vi In order to arrive at a solution for any systems of interest several assumptions must be made: 3. which produces a new set of functions φi eff 4. which produces a new potential Vi Born Oppenheimer Approximation: the nuclear and electronic portions of the ... wavefunction can be treated separately. Because electrons are much lighter than nuclei, they move much more rapidly and respond essentially instantaneously to changes in This procedure is repeated until the functions φi no longer change (converge) and produce nuclear position a self-consistent field (SCF). SCF convergence is a necessity for energy calculations. Ψ(R1...Rn,r1...rn) = Φ(R1...Rn)ψ(r1...rn) – Φ is a wavefunction for nuclei and a function of nuclear positions R – ψ is a wavefunction for electrons and a function of electron positions r Linear combination of atomic orbitals (LCAO): electronic wavefunctions φi are molecular orbitals that span the entire molecule. As a further simplifying approximation, molecular We can now specify the electronic energy of a molecule as a function of fixed nuclear (atomic) positions. This forms a potential energy surface (PES) which is a 3N-6 (N = # of orbitals are constructed as the sum of atomic orbitals χu atoms) dimentional surface describing the energy as a function of nuclear positions One Electron Wavefunction: the electronic wavefunction ψ, which is dependant on all electons can be represented as the product of individual one electron wave functions Because HF theory uses an effective electron-electron repulsion term, HF ψ(r1...rn) = φ1(r1)φ2(r2)...φn(rn) energy, EHF will always be greater than the exact energy E. The instantaneous electron-electron repulsion is referred to as electron coorelation: In order for this formulation to solve the Schrödinger equation the effect of electron- electron repulsion must be dealt with. To do this Hartree substituted the exact e-e Ecorr = E – EHF eff repulsion with an effective repulsion Vi . The exact e-e repulsion is replaced with an effective field produced by the average positions of remaining electrons. This is a This is the best-case error of HF theory major assumption. 3 Baran Lab Steven McKerrall Modern Computational Organic Chemistry Group Meeting Basis Functions & Basis Sets A single basis function is typically made up of multiple gaussian functions (GTOs) The Hartree-Fock limit, EHF, is reached only for an infinite set of atomic orbitals. in order to correct for deviations from STOs Because an inifinite set of orbitals is computationally impractical, some finite set of functions must be used to represent the atomic orbitals. This is referred to as Pople notation: for commonly employed split-valence basis sets the number of gaussian the Basis Set. functions (primatives) is described by the name The most logical starting point is to use an exact solution to the Schrödinger equation Valence For Carbon: for a hydrogen atom, a Slater-type orbital (STO). STOs are extremely problematic for double zeta computation, however, and so the use of Gaussian-type orbitals (GTO) was proposed. 6-31G Core single zeta inner outer For carbon the 6-31G basis set contains 9 basis functions (1 core, 8 valence). Each core basis function is made up of 6 GTOs, each inner valence function is made up of 3 GTOs and each outer valence function is made up of 1 GTO (22 GTOs total) Polarization functions: Because GTOs still lack some flexibility to describe electron distribution a set of polarization functions are typically added. These are typically d orbitals for heavy atoms and p orbitals for Hydrogen. The functions are not identical and so to better mimic a STO multiple GTOs are used to Carbon: mimic each STO. 6-31G(d): six d-type (Cartesian) basis functions added