Methods and applications in Quantum Chemistry, Life Science and Drug Design software. David Tur, PhD Scientific Applications expert

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1 Methods and applications in Quantum Chemistry, Life Science and Drug Design software David Tur, PhD Scientific Applications expert

2 Methods and applications in Quantum Chemistry, Life Science and Drug Design software I. Introduction II. Theoretical Chemistry III. Computational Chemistry Methods IV. From theory to practice: Software at CESCA V. Drug Design software

3 Introduction Computational chemistry simulates chemical structures and reactions numerically, based in full or in part on the fundamental laws of physics. Foresman and Frisch The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be solvable. Paul Dirac

4 I. Introduction II. Theoretical Chemistry III. Computational Chemistry Methods IV. From theory to practice: Software at CESCA V. Drug Design software

5 Theoretical Chemistry Theoretical Chemistry is defined as the mathematical description of chemistry. When these mathematical methods are sufficiently well developed to be automated and implemented on a computer, we can talk about Computational Chemistry

6 Theoretical Chemistry Theoretical Chemistry is defined as the mathematical description of chemistry. When these mathematical methods are sufficiently well developed to be automated and implemented on a computer, we can talk about Computational Chemistry Very few aspects of chemistry can be computed exactly, but almost every aspect of chemistry has been described in a qualitative or approximate quantitative computational scheme

7 Theoretical Chemistry Theoretical Chemistry is defined as the mathematical description of chemistry. When these mathematical methods are sufficiently well developed to be automated and implemented on a computer, we can talk about Computational Chemistry Very few aspects of chemistry can be computed exactly, but almost every aspect of chemistry has been described in a qualitative or approximate quantitative computational scheme The theoretical chemist must keep in mind that numbers obtained from theoretical calculations are not exact (they use many approximations), but they can offer an useful insight into real chemistry

8 Theoretical Chemistry What can we predict with modern Theoretical Chemistry: Geometry of a molecule Dipole moment Energy of reaction Reaction barrier height Vibrational frequencies IR spectra NMR spectra Reaction rate Partition function Free energy Any physical observable of a small molecule

9 Theoretical Chemistry

10 Theoretical Chemistry Computational Chemistry methods

11 Theoretical Chemistry Computational Chemistry methods

12 Theoretical Chemistry Computational Chemistry methods

13 Theoretical Chemistry Computational Chemistry methods

14 I. Introduction II. Theoretical Chemistry III. Computational Chemistry Methods IV. From theory to practice: Software at CESCA V. Drug Design software

15 Computational Chemistry methods Different models use different approximations (or levels of theory) to produce results of varying levels of accuracy. There is a trade off between accuracy and computational time.

16 Computational Chemistry methods Different models use different approximations (or levels of theory) to produce results of varying levels of accuracy. There is a trade off between accuracy and computational time. There are two main types of models depending on the starting point of the theory: Classical methods, are those methods that use Newton mechanics to model molecular systems. Quantum Chemistry methods, which makes use of quantum mechanics to model the system. These methods use different type of approximation to solve the Schrödinger equation.

17 Computational Chemistry methods Classical methods Quantum methods Molecular Mechanics Semi-empirical methods DFT Wavefunction based methods GGA LDA LSDA HF&MCSCF hybrid-gga meta-gga SR MR Hybrid-meta-GGA MP2 Post-HF Coupled Cluster CASPT2 FCI MRCI

18 Computational Chemistry methods Introduction Molecular mechanics Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT Basis sets Computational chemistry methods in solid state Conclusions

19 Computational Chemistry methods Introduction Molecular mechanics Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT Basis sets Computational chemistry methods in solid state Conclusions

20 Molecular Mechanics Molecular Mechanics (MM) use the laws of classical physics to predict structures and properties of molecules The motions of the nuclei are studied and the electrons are not explicitly treated (Born-Oppenheimer approximation) Molecules are seen as a mechanical assemblies made up of simple elements like balls (atoms), sticks (bonds) and flexible joints (bond angles and torsion angles) MM treats molecules as a collection of particles held together by a simple harmonic forces. These harmonic forces are described in terms of individual potential functions. The overall molecular potential energy or steric energy of the molecule is the sum of the potential functions of its constituents.

21 Computational Chemistry methods 1. Introduction 2. Molecular mechanics 3. Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT 4. Basis sets 5. Computational chemistry methods in solid state 6. Conclusions

22 Molecular Mechanics With this assumptions, the Mechanics equation can be simply written as: E=E B +E A +E D +E NB where E B is the energy involved in the deformation of a bond, either by stretching or compression, E A is the energy involved in angle bending, E D is the torsional angle energy, and E NB is the energy involved in interactions between atoms that are not directly bonded. *Picture from the NIH site of Molecular modelinghttp://cmm.cit.nih.gov/modeling/

23 Molecular Mechanics The exact functional form of the potential function of Force Field depends on the program being used. Bond and angle terms are generally modeled as harmonic potentials centered around equilibrium bond-length values (derived from exp. or ab initio calculations). Morse potential is an alternative that results in more accurate results of vibrational spectra but at higher computational cost. The dihedral terms shows multiple minima and thus can not be modeled as harmonic oscillators. The Non Bonded interactions are much more computationally costly to calculate, and different approaches are used to model them. This term is divided between short range interactions (VdW) usually modeled using Lennard-Jones potential and long range or electrostatic interactions, whose basic functional is the Coulomb potential.

24 Molecular Mechanics General form of the Molecular Mechanics equations:

25 Molecular Mechanics *Picture from the Wikipedia: Molecular Modelling

26 Molecular Mechanics Molecular Mechanics computations are quite inexpensive (compared to ab initio methods), and they allow to be used to compute properties for very large systems containing many thousands of atoms such as: Energy optimization (combined with simulated annealing, Metropolis, or other MC methods) Calculation of binding constants Simulating of protein folding kinetics Examination of active site coordinates Design of binding sites However it carries two main limitations: Each force field achieves good results only for limited class of molecules related to those for which it was parameterized. The neglecting of electrons means that MM methods can not treat chemical problems where electronic effects are dominant (bond formations, bond breaking )

27 Introduction to Computational Chemistry 1. Introduction 2. Molecular mechanics 3. Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT 4. Basis sets 5. Computational chemistry methods in solid state 6. Conclusions

28 Quantum Chemistry Methods Classical methods Quantum methods Molecular Mechanics Semi-empirical methods DFT Wavefunction based methods GGA LDA LSDA HF&MCSCF hybrid-gga meta-gga SR MR Hybrid-meta-GGA MP2 Post-HF Coupled Cluster CASPT2 FCI MRCI

29 Quantum Chemistry Methods Where did ab initio methods finished in this scheme? Ab initio is Latin for from the beginning, and indicates that the calculation is from first principles and that no empirical data is used. Are DFT ab initio methods? Rigorously speaking DFT should be considered an ab initio method, but as the most common functionals use parameters derived from empirical data, or from more complex calculations, it has historically been grouped apart from ab initio methods. Here we will difference between wave function based methods and Density functional Theory (within ab initio methods).

30 Quantum Chemistry Methods Quantum Chemistry is a branch of theoretical chemistry that applies Quantum Mechanics in order to mathematically describe the fundamental properties of atoms and molecules. The complete knowledge of the chemical properties of the system implies computing the wave function that describes the electronic structure of these atoms and molecules. In 1925 Erwin Schrödinger analyzed what an electron would look like as a wavelike particle around the nucleus of the atom. From this model he formulated his equation for particle waves, which is the starting point of the quantum mechanical study of the properties of an atom or molecule: Ψ ih = t H Ψ where H is the Hamiltonian and Ψ is the wavefunction associated with the state of the system.

31 Quantum Chemistry Methods The main problem now is the solution of the electronic Schrödinger equation. The exact solution to this equation is not known (apart from monoelectronic systems), numerical methods must be used to solve it. Quantum chemistry addresses the solution of this problem in different ways, depending on the mathematical approaches used. These methods are based on theories which range from highly accurate, but suitable only for small systems, to very approximate, but suitable for very large systems.

32 Quantum Chemistry Methods The Schrödinger model is based on the six postulates of quantum mechanics: 1. Associated with any particle moving in a conservative force field is a wavefunction Ψ x, t, which contains all information that can be known about the system. 2. For every observable in classical mechanics, a linear Hermitian operator is defined 3. When measuring the observable associated with the operator A in ÂΨ = aψ, the only values that will ever be observed are the eigenvalues a which satisfy ÂΨ = aψ 4. The average value of the observable corresponding to operator is given by: Â = * Ψ ÂΨdr * Ψ Ψ 5. The wavefunction evolves in time according to the time-dependent Schrödinger equation: dr Ψ H Ψ ( r, t ) = ih t 6. The total wavefunction must be antisymmetric with respect to the interchange of all coordinates of one fermion with those of another. The electronic spin must be included in this set of coordinates. The Pauli Exclusion Principle is a direct result of this antisymmetry principle. ( )

33 Quantum Chemistry Methods The most commonly used quantum chemistry methods are: 1.- Ab initio methods, where the solution of the Schrödinger equation is obtained from first principles of quantum chemistry using rigorous mathematical approximations, and without using empirical data.in the frame of ab initio methods there are two strategies to solve equation: Wavefunction based methods, which are based on obtaining the wavefunction of the system, Density functional based methods, that consist in the study of the properties of the system through its electronic density, but avoiding the explicit determination of the electronic wavefunction. 2.- Semi-empirical methods, which are less accurate methods that use experimental results to avoid the solution of some terms that appear in the ab initio methods.

34 Wave function based methods The first and most relevant ab initio method is the Hartree-Fock theory, which was first introduced in 1927 by D.R. Hartree. The procedure, which he called self-consistent field (SCF), is used to calculate approximate wavefunctions and energies for atoms and ions. The HF method assumes that the exact, N-body wavefunction of the system can be approximated by a single Slater determinant (fermions) or by a single permanent (bosons) of N spin-orbitals. The starting point for the HF method is a set of approximate one-electron wavefunction, (orbitals). For a molecular or crystalline calculation the initial approximate one-electron wavefunctions are typically a LCAO (linear combination of atomic orbitals) Using variational principle (HF upper bound to true ground state energy), we can derive a set of N-coupled equations for the N spin orbitals. The minimization of the HF energy expression with respect to changes in the orbtials, by applying Langrange method of undetermined multiplieres, yields the HF equations defining the orbitals.

35 Wave function based methods Brief mathematical exposition of HF theory: 1-Wavefunction written as a single determinant Ψ = ( φ φ φ ) det 1, 2... N 2-The electronic Hamiltonian can be written as: el ( ) (, ) H = h i + v i j i i< j where h(i) and ν(i,j) are the one and two electrons operator defined as: 1 2 Z 1 A h( i) = i v( i, j) = 2 r r Eel A ia 3-The electronic energy of the system is given by : = Ψ H el Ψ 4-The resulting HF equations from minimization of the energy: ( ) χ ( ) = ε χ ( ) f x x x 1 i 1 i i 1 where ε i is the energy value associated with orbital χ i and f is defined as ( ) = ( ) + j ( ) j ( ) f x h x J x K x j ij

36 Wave function based methods ( ) = ( ) + j ( ) j ( ) f x h x J x K x j where J i found in the second term of the equation is the so-called Coulomb term that gives the average local potential at point x due to the charge distribution from the electron in orbital χ i and is defined as: ( x ) 2 χ 2 1 J j ( x1 ) χi ( x1 ) = χi ( x2 ) dx2 = χ j x2 χ j x2 χi x1 r12 r12 ( x ) χ ( x ) ( ) ( ) ( ) and K i third operator term of the equation, is the exchange operator that is defined as: χ K x x x dx x x x * j 2 i 2 1 j ( 1) χi ( 1) = χ j ( 1) 2 = χ j 2 χi 2 χi 1 r12 r12 ( ) ( ) ( ) The Hartree-Fock equations can be solved numerically or in the space spanned by a set of basis functions (Hartree-Fock-Roothan equations) Some guess of the initial orbitals is required, and then theses orbitals are refined iteratively (self-consistent-field approach, SCF), finally obtaining the form and energy.

37 Wave function based methods Greatly simplified algorithmic flowchart illustrating the Hartree-Fock Method. *Flowchart from Wikipedia: Hartree-Fock

38 Wave function based methods The error in the determination of the total energy due to the use of the Hartree- Fock method is the so-called correlation energy: Ecorr = Eo EHF where E 0 is the is the exact nonrelativistic energy of the system and E HF is the energy in the Hartree-Fock limit (this limit is obtained by carrying out HF calculations using an infinite basis set). There have been a large number of methods developed to improve the Hartree-Fock results, all accounting for the correlation energy in one way or another, the so-called Post-HF methods.

39 Wave function based methods Hartree-Fock method makes five major simplifications in order to deal with this task: The Born-Oppenheimer approximation is inherently assumed. The full molecular wavefunction is actually a function of the coordinates of each of the nuclei, in addition to those of the electrons. Typically, relativistic effects are completely neglected. The momentum operator is assumed to be completely non-relativistic. The variational solution is assumed to be a linear combination of a finite number of basis functions, which are usually (but not always) chosen to be orthogonal. The finite basis set is assumed to be approximately complete. Each energy eigenfunction is assumed to be describable by a single Slater determinant, an antisymmetrized product of one-electron wavefunctions (i.e., orbitals). The mean field approximation is implied. Effects arising from deviations from this assumption, known as electron correlation, are completely neglected. Relaxation of the last two approximations give rise to many post-hartree-fock methods.

40 Wave function based methods Single reference (SR) methods: use a single Slater determinant as a zero order wavefunction or starting point to generate the excitation states used to describe the system. Multireference methods (MR): where the systems need to be described by more than one electronic configuration (e.g. for molecular ground states that are quasi-degenerate with low-lying excited states, or in bond-breaking situations) Quantum methods Wavefunction based methods HF&MCSCF While the HF wavefunction is uniquely defined by specifying the number of occupied orbitals in each symmetry, in the MCSCF (multi configurational SCF) the electronic state of the system is approximated by a multi-configuration wavefunction MP2 FCI SR Coupled Cluster Post-HF MR CASPT2 MRCI

41 Wave function based methods Single reference Post-HF methods: Configuration Interaction (CI): a variational method that accounts for the correlation energy using a variational wavefunction, which is a linear combination of determinants or configuration state functions built form spin orbitals (SO). If the expansion includes all possible configurations of the appropriate symmetry, then this is a full configuration interaction (FCI) procedure which exactly solves the electronic Schrödinger equation within the space spanned by the one-particle basis set. In practice not all the unoccupied Hartree-Fock orbitals can be computed, The expansion in must be truncated, not considering any excitations above a given order. When the expansion is truncated at the zeroth order, the Hartree-Fock method is recovered. At first order truncation the Configuration Interaction with only Single excitations (CIS) is obtained, at second order CI with Single and Double excitations (CISD), and so on: CISDT (third order), CISDTQ (fourth order), etc.

42 Wave function based methods Single reference Post-HF methods: Møller-Plesset (MP): This is a perturbational method. Møller-Plesset perturbation theory adds electron correlation to the Hartree-Fock method by means of Rayleigh-Schrödinger perturbation theory (RSPT). In RS-PT one considers an unperturbed Hamiltonian operator H 0 to which is added a small (often external) perturbation V: where λ is an arbitrary real parameter. In MP theory the zeroth-order wave function is an exact eigenfunction of the Fock operator, which thus serves as the unperturbed operator. The perturbation is the correlation potential.in RS-PT the perturbed wave function and perturbed energy are expressed as a power series in λ: Substitution of these series into the time-independent Schrödinger equation gives a new equation: Equating the factors of λ k in this equation gives an kth-order perturbation equation.

43 Wave function based methods Single reference Post-HF methods: Coupled Cluster (CC) theory: is another numerical technique used for describing manybody systems starting from HF molecular orbital and adding correcton terms to take into account electron correlation. The coupled cluster methodology employs an excitation operator T in a analogous form as C in CI theory that has the form: operator used to construct the new molecular wavefunction starting from HF MO used to find an approximate solution to the Schrödigner equation After some farragous algebre, the correlatino energy is obtainded from the CC equations: Depending on the highest number of excitations allowed in the definition of T we obtain different CC methods: CCSD, CC3, CCSD(T), CCSDTQ

44 Wave function based methods Single reference Post-HF methods: Chart arranged in order of increasing accuracy, when increasing the level of correlation, and the size of the basis sets. FCI FCI/ STO-3G FCI/ 3-21G FCI/ 6-31G* FCI/ 6-311G(2df) EXACT CCSD(T) CCSD(T)/ STO-3G CCSD(T)/ 3-21G CCSD(T)/ 6-31G* CCSD(T)/ 6-311G(2df) CCSD(T) CBS CCSD CCSD/ STO-3G CCSD/ 3-21G CCSD/ 6-31G* CCSD/ 6-311G(2df) CCSD CBS MP2 MP2/ STO-3G MP2/ 3-21G MP2/ 6-31G* MP2/ 6-311G(2df) MP2 CBS HF HF/ STO-3G HF/ 3-21G HF/ 6-31G* HF/ 6-311G(2df) HF CBS STO-3G 3-21G 6-31G* 6-311G(2df) CBS *Head-Gordon, J. Phys. Chem. Vol. 100, No, 31, 1996

45 Wave function based methods Multi-reference Post-HF methods: The most commonly used MCSCF approach, which simplifies the selection of configurations needed to construct a proper wavefunction, is the so-called Complete Active Space Self Consistent Field method (CASSCF). In a CASSCF wavefunction the occupied orbital space is divided into a set of inactive orbitals and a set of active orbitals. All inactive orbitals are doubly occupied (closed shell) in each Slater determinant. In contrast, the active orbitals have varying occupations, and all possible Slater determinants are taken into account distributing electrons in all possible ways among the active orbitals corresponding to a full CI in the active space. Starting from MCSCF, are obtained MRCI methods (analogous to CI using HF), or CASPT2 (analogous to MP2 for SR methods).

46 Semi-empirical empirical Methods Semi-empirical quantum methods, represents a middle road between the mostly qualitative results available from molecular mechanics and the high computationally demanding quantitative results from ab initio methods Semi-emipirical methods attempt to address two limitations of the Hartree- Fock calculations, such as slow speed and low accuracy, by omitting or parameterizing certain integrals Integral approximation: there are three principal levels of integral approximations: Complete Neglect of Differential overlap (CNDO) Intermediate Neglect of Differential Overlap (INDO) Neglect of Diatomic Differential Overlap (NDDO) (Used by PM3, AM1 ) the integrals at a given level of approximation are either determined directly from experimental data or calculated from corresponding analytical formula with ab initio methods or from suitable parametric expressions. Semi-empirical methods are very fast, give accurate results when applied to molecules that are similar to those used for parametization, and are applicable to very large molecular systems

47 Density Functional Theory Density functional theory (DFT): is an alternative approach to study the electronic structure of many-body systems that over the past years has strongly influenced the evolution of Quantum Chemistry. DFT expresses the ground state energy of the system in terms of total one-electron density rather than making use of the wavefunction. The DFT formalism has the same starting point as the wavefunction based methods, that is the Born-Oppenheimer approximation where the nuclei of the treated molecules are seen as fixed, coupled with an extenal potential, V ext, where the electrons are moving. The Hamiltonian can now be rewritten as H = F + V ext where F is the sum of the kinetic energy of the electrons, and the electron-electron Coulomb interaction In the DFT approach, the key variable is the particle density, and for this Hamiltonian, the ground state gives rise to a ground state electronic densityρ 0 (r) defined as: ( r) = Ψ Ψ = dr Ψ ( r, r, r, K, r ) 2 ρ ρ = i i 2 N Thus the ground state wavefuntion and density ρ 0 (r), are both functionals of the external potential and the number of electrons and N. N

48 Density Functional Theory Starting from here Hohenberg-Kohn (HK) made two remarkable statements that are the basis of the modern employed DFT methods: Theorem 1: The external potential V ext, and hence the total energy, is a unique functional of the electron density ρ(r) Theorem 2: The groundstate energy can be obtained variationally: the density that minimises the total energy is the exact groundstate density. Appling these theorems, and after some more farragoes mathematics, the form of the Schrödinger equation is: 1 2 V ( r) ( r) ε ψ ( r) 2 + KS ψ i = i i where the Khon-Sham potential, V KS, has the ρ( r ') VKS ( r) = dr ' + VXC ( r) + Vext ( r) r r ' Since the Kohn-Sham potential V KS (r) depends upon the density, it is necessary to solve these equations self-consistently as in the Hartree-Fock scheme

49 Density Functional Theory There are many different ways to approximate this functional V XC, and to do this E XC is generally divided into two separate terms: E [ ρ] = E [ ρ] + E [ ρ] XC X C where E X is the exchange (int. e - same spin) term and E C the correlation (int. e - opposite spin) term. It is important to note that although Kohn-Sham is an exact method in principle, because of the unknown exchange-correlation functional V XC it turns out to be approximate. FINDING THE APPROPIATE FUNCTIONAL: From LDA (local density approximation), to modern meta-hybrid-gga (Generalized Gradient approximation)

50 Density Functional Theory The development of GGA functionals has followed two main lines, the non-empirical and the semi-empirical approach. The typical non-empirical approach, favored in physics, is to construct a functional subject to several exact constraints. This strategy can be viewed as a ladder with five rungs, from the Hartree theory (the earth) to the exact exchange and correlation functional (heaven), as follows: HEAVEN (chemical accuracy) rung 5 fully nonlocal explicit dependence on unoccupied orbitals rung 4 hybrid functionals explicit dependence on occupied orbitals rung 3 meta-ggas explicit dependence on kinetic energy density rung 2 GGAs explicit dependence on density gradients rung 1 LDA local density only EARTH (Hartree theory) Although Jacob s ladder is historically presented as the starting point for the formulation of the non-empirical approaches, both semi-empirical and non-empirical functionals can be assigned to various rungs of the ladder.

51 Introduction to Computational Chemistry 1. Introduction 2. Molecular mechanics 3. Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT 4. Basis sets 5. Computational chemistry methods in solid state 6. Conclusions

52 Basis sets In Mathematics: a basis set is a collection of vectors that spans a vectorial space where a numerical problem is solved. In quantum chemistry: the wavefunctions are the mathematical description of where an electron or group of electrons are, and basis sets represent the wavefunction that allow the Schrödinger equation via any of the methods previously explained Types of basis functions: Slater type basis set (STO): a set of functions which decayed exponentially with distance from the nuclei. ( ) 1 ξ r,, = Nr e Y (, ) φ θ ϕ θ ϕ STO n r ξ, n, l, m l, m Gaussian type basis sets (GTO): STO are approximated as linear combination of gaussian type orbitals. 2 (2 1) ξ ( r,, ) = Nr e Y (, ) φ θ ϕ θ ϕ GTO n n r ξ, n, l, m l, m GTO have the advantage over STO in that it is much easier to calculate integrals analytically, and thus are huge computational savings, but the exponential dependence on r 2 means that in contrast to STO, the maximum at the nucleus is not in fact well described

53 Basis sets There are two main families of basis set used in modern computational chemistry calculations: Pople family of basis set: X-Y Y (+)G(p) where Ys indicates the number of Gaussians that compose the valence orbitals, and the Y itself represents the number of linear combinations of primitive Gaussians that compose each Gaussians. The number of polarized functions added is given by the p in brackets after the G, and these basis set can also be improved by adding diffuse functions for non-hydrogen atoms (+) or also for hydrogen (++). e.g.: 3-21G, 6-31G(d), G(d,p) Correlation consistent basis set: cc-pvxz where X indicated the number of basis functions composing the valence orbitals (X=D,T,Q are double, triple or quadruple zeta respectively). Difuse functions introduced with aug- prefix e.g.: cc-pvdz, aug-cc-pvqz

54 Introduction to Computational Chemistry 1. Introduction 2. Molecular mechanics 3. Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT 4. Basis sets 5. Computational chemistry methods in solid state 6. Conclusions

55 Computational chemistry methods in solid state Computational chemistry methods in solid state follow the same approach as they do for molecule but can introduce two different approaches: Translation symmetry: The electronic structure of a crystal is in general described by a band structure, which defines the energies of electron orbitals for each point in the Brillouin zone. Ab initio and semi-empirical calculations yield orbital energies, therefore they can be applied to band structure calculations. Plane waves basis set: Completely delocalized basis functions as an alternative to the molecular atom-centered basis functions. Common choice for prediction properties in crystals

56 Introduction to Computational Chemistry 1. Introduction 2. Molecular mechanics 3. Quantum chemistry methods I. Wave function based methods Hartree-Fock Post-HF Methods II. Semi-empirical methods III. DFT 4. Basis sets 5. Computational chemistry methods in solid state 6. Conclusions

57 Conclusions in Computational Chemistry Methods Method Type Advantages Disadvantages Best for Molecular Mechanics Semi-Empirical uses classical physics relies on force-field with embedded empirical parameters uses quantum physics and experimentally derived empirical parameters uses approximation extensively Computationally least intensive - fast and useful with limited computer resources can be used for molecules as large as enzymes less demanding computationally than ab initio methods capable of calculating transition states and excited states particular force field applicable only for a limited class of molecules does not calculate electronic properties requires experimental data (or data from ab initio) for parameters requires experimental data (or data from ab initio) for parameters less rigorous than ab initio) methods large systems (thousands of atoms) systems or processes with no breaking or forming of bonds medium-sized systems (hundreds of atoms) systems involving electronic transitions Ab Initio uses quantum physics mathematically rigorous, no empirical parameters uses approximation extensively useful for a broad range of systems does not depend on experimental data capable of calculating transition states and excited states computationally expensive small systems systems involving electronic transitions molecules or systems without available experimental data ("new" chemistry) systems requiring rigorous accuracy

58 Conclusions in Computational Chemistry Methods Method Current computational dependence on molecular size, M Current estimate of maximum feasible molecular size FCI Factorial 2 atoms (15) CCSD(T) M atoms (20-50) CCSD M atoms (100) MP2 M atoms (50-150) Current scalings of electronic structure methods with molecular size, M and estimates of the maximum molecular sizes (in terms of numbers of first-row nonhydrogen atoms) or which energy and gradient evaluations can be tackled by each method at present * In blue (in brackets) actualization of this estimations to 2009 computational available resources. These results must be taken into account due to the dependence of the calculation with the size of the basis set used. HF, KS-DFT M 2- M atoms (50-300) *Head-Gordon, J. Phys. Chem. Vol. 100, No, 31, 1996

59 Conclusions in Computational Chemistry Methods Overall, the main conclusion that emerges from this talk is that it is possible to simulate different properties of interest for chemists (biologists, pharmaceutics, physics ) applying computational chemistry, with reasonable cost and saving much experimental time in the laboratory. The key point is to select which is the best method to be used depending on the computational resources available and the desired accuracy.

60 I. Introduction II. Theoretical Chemistry III. Computational Chemistry Methods IV. From theory to practice: Software at CESCA V. Drug Design software

61 From theory to practice: available software Package Altix CP4000 NovaScale Altix UV License Allowed users ADF x x x x Commercial Academic Amber x x x x* Commercial Academic AutoDock x x x x GNU GPL All CPMD x x x Free (non-profit) Academic DL_POLY x x x x* Free academic lic. Academic Gamess (US) x x x x Free academic lic. Academic Gaussian x x x x Commercial All GROMACS x x x x* Free All Jaguar x x x* Commercial All (1) MOPAC x x x* Free non-profit Academic NAMD x x x x* Free All NWChem x x x Free academic lic. Academic POLYRATE x x x Free All TURBOMOLE x x x* Commercial Acad.(3 Univ.) SIESTA x x x Free academic lic. Academic * Coming Soon!!!!

62 Molecular mechanics Uses classical physics Relies on force-field with embedded empirical parameters Advantages Disadvantages Best for Computationally least intensive - fast and useful with limited computer resources Can be used for molecules as large as enzymes Particular force field applicable only for a limited class of molecules Does not calculate electronic properties Requires experimental data (or data from ab initio) for parameters Large systems (thousands of atoms) Systems or processes with no breaking or forming of bonds

63 Molecular Mechanics Package Available versions Characteristics MM only Amber 7/8/9/10 Bio. /Par. Dec./ DL_POLY 2.1x/3.0x Bio&nonBio/Par.Dc Gromacs Bio./Par.Dec NAMD 2.5/2.6/2.7b1 Bio. General Purpose Gaussian G03C2/G03D2/G03E1/G09A2/G09B1 Gamess (US) 2004/2005/2006/2008/2009/2010 Bio./Serial Code Jaguar 6.5/7.0/7.5 NWChem 4.7/5.0/5.1.1/6.0 Bio TURBOMOLE 6.0 Availabe trough SDF Macromodel (Schrödinger 2009 suite) Prime (Schrödinger 2009 suite) Bio: Designed mainly for biological systems; Par. Dec: parallelized using atom decomposition

64 Semiempirical Uses quantum physics and experimentally derived empirical parameters Uses approximation extensively Advantages Disadvantages Best for Less demanding computationally than ab initio methods Capable of calculating transition states and excited states Requires experimental data (or data from ab initio) for parameters Less rigorous than ab initio) methods Medium-sized systems (hundreds of atoms) Systems involving electronic transitions

65 Semiempirical Package Available versions Available methods Semiempirical only MOPAC 2007 AM1, PM3, MNDO, MNDO/d, RM1 i PM6 General Purpose Gaussian G03C2/G03D2/G03E1/G09A2/G09B1 CNDO, INDO, MINDO/3,MNDO, AM1, PM3, PM6 Gamess (US) 2004/2005/2006/2008/2009/2010 MNDO, AM1,PM3

66 Ab initio Uses quantum physics Mathematically rigorous, no empirical parameters Uses approximation extensively Advantages Disadvantages Best for Useful for a broad range of systems Does not depend on experimental data Capable of calculating transition states and excited states Computationally expensive Small systems Systems involving electronic transitions Molecules or systems without available experimental data ("new" chemistry) Systems requiring rigorous accuracy

67 HF and Post-HF Package Available methods Parallel Gamess (US) Gaussian Jaguar HF (RHF, ROHF, UHF, GVB), SCF,MCSCF,CASSCF, CI, MRCI Coupled cluster (closed shells) MP2,ROMP2,UMP2, MCQDPT(CASSCF-MRMP2) HF(RHF, UHF, ROHF), SCF,MCSCF,CASSCF, RASSCF,MP2,MP3,MP4,MP5,CI,CID,CISD,CCD, CCSD,CCISD,G1,G2,G2(MP2),G3,G3(MP2), GVB-PP HF(RHF, ROHF, UHF, GBV) MP2, LMP2 GVB-RCI, GBV-LMP2, GVB-DFT MPI OpenMP MPI NWChem HF(RHF,ROHF,UHF),SCF,CASSCF,CCSD(T),CC SDTQ, Plane wave, non-canonical MP2, MP3,MP4 MPI

68 Density Functional Theory Package Available versions Parallel DFT only ADF / / / / MPI CPMD /3.9.1/ MPI Jaguar 6.5/7.0/7.5 MPI SIESTA 2.0.1/2.0.2/3.0-rc2 MPI General Purpose Gaussian G03C2/G03D2/G03E1/G09A2/G09B1 OpenMP Gamess (US) 2004/2005/2006/2008/2009/2010 DDI/MPI NWChem 4.7/5.0/5.1.1 MPI

69 I. Introduction II. Theoretical Chemistry III. Computational Chemistry Methods IV. From theory to practice: Software at CESCA V. Drug Design software

70 Drug Design software 7 laboratories and 9 academic groups (2) (2)

71 Drug Design software Used hours Licenses Ending at Tripos Sybyl wildcard (acad. + ind.) Schrödinger academic tokens industrial tokens Sybyl Schrödinger

72 Tripos software Sybyl 7.3 Sybyl (1) Unity Base (1) Network (1-5) Legion (1) 1 Wildcard LeapFrog* Selector* AdvancedCOMFA* DiverseSolution* CombilibMaker*

73 Schrödinger software Schrödinger (Suite 2010) 34 tokens acad. Macromodel (2) LigPrep (1) Liason (4) MINTA (1) QickProp (2) Epik (1) ConfGen (1) SiteMap (1) Jaguar (2) Strike (1) Prime (8) Glide (5) Phase (1) (5) CombiGlide (1) (5) Qsite (1) (4) XP Visualizer (1) Database: Phase database: Asinex, Bionet, Enamine, LifeChem, Maybridge, Specs and TimTec

74 How to apply for the Drug Design service Academic applications: Submitted through the Vicerrectorat de Recerca of your own institution Prices for 2010 : (allows unlimited access to all the software) Initial fee: 227 (only paid once) Annual fee: Additional information: sdf@cesca.es

75 Methods and applications in Quantum Chemistry, Life Science and Drug Design software Thank you for your attention!!! QUESTIONS???? David Tur, PhD Scientific Applications expert