Introduction to Computational Chemistry

Introduction to Computational Chemistry
10/1/2007 Introduction to Computational Chemistry Shubin Liu, Ph.D. Renaissance Computing Institute University of North Carolina at Chapel Hill This is the first session of a seriers of trainings on computational chemistry. The purpose of this session is to give a general idea of how the current framework of computational chemistry looks like, what kinds of methods are available and what we can do with them. Renaissance Computing Institute, UNC-CH

10/1/2007 Outline Introduction Methods in Computational Chemistry Ab Initio Semi-Empirical Density Functional Theory New Developments (QM/MM) Hands-on Exercises After a brief introduction of what computational chemistry is about, we will focus today on one of the three major pieces of computational chemistry methods, namely approaches based on solving time-independent Schroedinger equation. Three major directions, ab initio, semi-empirical, and density functional theory, will be introduced. At the end, we will briefly mention two new developments, i.e., QM/MM and linear scaling methods. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Goals of Course To get familiar with computational chemistry methods available To serve as the starting point for further reading and applications Hands-on experiments via G03/GaussView The purpose of this training is to get familiar with the available computational chemistry approaches and serve as the starting point to further reading and pursuit of real applications to physics, chemistry, biology, etc. related problems in the future. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Prerequisites UNIX & LSF basics Basic kernel commands (e.g., ls, cd, more, vi, rm, …, bsub, bjobs, …) Introduction to Scientific Computing Introduction to Gaussian/GaussView An account on Emerald cluster with csh/tcsh Shell (type “echo $SHELL”) Though not mandatory, these prerequisites apply to this course. At least with these knowledge in place, you will have a relatively easier time to go through the materials presented hereafter. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

About Us ITS Physical locations: 401 West Franklin Street; 211 Manning Drive 12 Divisions IT Infrastructure and Operations Research Computing Teaching and Learning Technology Planning and Special Projects Telecommunications User Support and Engagement Office of the Vice Chancellor Communications Enterprise Applications Enterprise Data Management Financial Planning and Human Resources Information Security RENCI Anchor Site: 100 Europa Drive, suite 540, Chapel Hill A number of virtual sites on the campuses of Duke, NCSU and UNC-Chapel Hill, and regional facilities across the state Mission: to foster multidisciplinary collaborations; to enable advancements in science, industry, education, the humanities and the arts; to provide the technical leadership and expertise; to work hand-in-hand with businesses and communities to utilize advanced technologies 10/1/2007 Introduction to Computational Chemistry

About Us Where/Who are we and do we do? ITS Manning: 211 Manning Drive Website Groups Infrastructure Engagement User Support 10/1/2007 Introduction to Computational Chemistry

10/1/2007 About Myself Ph.D. from Chemistry, UNC-CH Currently Senior Computational Scientist Renaissance Computing Institute at UNC-CH Responsibilities: Support Comp Chem/Phys/Material Science software, Support Programming (FORTRAN/C/C++) tools, code porting, parallel computing, etc. Engagement projects with faculty members on campus Conduct own research on Comp Chem DFT theory and concept Systems in biological and material science 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

About You Name, department, group, research interest? Do you have any real problem that is intended to be studied by computational chemistry approaches? If yes, what is it? 10/1/2007 Introduction to Computational Chemistry

Think BIG!!! What is not chemistry? From microscopic world, to nanotechnology, to daily life, to environmental problems From life science, to human disease, to drug design Only our mind limits its boundary What cannot computational chemistry do? From small molecules, to DNA/proteins, 3D crystals and surfaces From species in vacuum, to those in solvent at room temperature, and to those under extreme conditions (high T/p) From structure, to properties, to spectra (UV, IR/Raman, NMR, VCD), to dynamics, to reactivity All experiments done in labs can be done in silico Limited only by (super)computers not big/fast enough! 10/1/2007 Introduction to Computational Chemistry

Central Theme of Computational Chemistry
10/1/2007 Central Theme of Computational Chemistry DYNAMICS REACTIVITY STRUCTURE CENTRAL DOGMA OF MOLECULAR BIOLOGY SEQUENCE  STRUCTURE DYNAMICS FUNCTION EVALUTION The central dogma (or theme) of computational chemistry, I think, is to try to understand following topics of any given molecular system. We are interested to understand its geometric and electronic structures first. After the structures are understood, we want to investigate its dynamic properties, how it behaves when it is put in certain environment like temperature, magnetic field, etc. More importantly, we wish to know what its potential energy surface looks like and how it behaves with it, especially when a chemical reaction takes place. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Multiscale Hierarchy of Modeling
10/1/2007 Multiscale Hierarchy of Modeling Other than a single molecules, computational chemistry methods are able to deal with a spectrum of problems with a spectrum of theoretical/computational approaches. For systems within the angstrom range, quantum mechanics is the choice. At the nano-micrometer level, molecular dynamics approach is the alternative. As the system size increases, we go through MESO and FEM kingdoms. Notice that between QM and MD regions, we do see an overlap. This is where the QM/MM method plays a role. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

What is Computational Chemistry?
10/1/2007 What is Computational Chemistry? Application of computational methods and algorithms in chemistry Quantum Mechanical i.e., via Schrödinger Equation also called Quantum Chemistry Molecular Mechanical i.e., via Newton’s law F=ma also Molecular Dynamics Empirical/Statistical e.g., QSAR, etc., widely used in clinical and medicinal chemistry So what is computational chemistry? No consensus has been available as to how to define it. It could be either narrowly/specifically or broadly defined. I prefer to define it as a discipline where following three components are included: QM, MD and statistical/empirical methods, each of which is based on a completely different methodology and way/algorithm of solving problems. Today, we only deal with the first component, quantum mechanics, based on the so-called Schrödinger equation. Focus Today 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

How Big Systems Can We Deal with?
10/1/2007 How Big Systems Can We Deal with? Assuming typical computing setup (number of CPUs, memory, disk space, etc.) Ab initio method: ~100 atoms DFT method: ~1000 atoms Semi-empirical method: ~10,000 atoms MM/MD: ~100,000 atoms For the QM method, given the current computing capability of a typical US university, such as that in UNC-Chapel Hill or ECU, how large molecular systems can we handle? It depends. Different levels of QM approaches can deal with different sizes of systems. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Starting Point: Time-Independent Schrodinger Equation
10/1/2007 Starting Point: Time-Independent Schrodinger Equation With this B-O approximation, we come to the time-independent Schrödinger equation, where the Hamiltonian includes variables from electrons only, whereas nuclei coordinates come in only as parameters. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Equation to Solve in ab initio Theory
10/1/2007 Equation to Solve in ab initio Theory Known exactly: 3N spatial variables (N # of electrons) To be approximated: 1. variationally 2. perturbationally This is the equation for all ab initio, semi-empirical and density functional theory methods to solve. H is the Hamiltonian of the system and Psi is its total electronic wavefunction, each of which has 3N spatial variables and N spin variables, a total of 4N, where N is the number of electrons. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Hamiltonian for a Molecule
10/1/2007 Hamiltonian for a Molecule kinetic energy of the electrons kinetic energy of the nuclei electrostatic interaction between the electrons and the nuclei electrostatic interaction between the electrons electrostatic interaction between the nuclei 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Ab Initio Methods Accurate treatment of the electronic distribution using the full Schrödinger equation Can be systematically improved to obtain chemical accuracy Does not need to be parameterized or calibrated with respect to experiment Can describe structure, properties, energetics and reactivity What does “ab intio” mean? Start from beginning, with first principle Who invented the word of the “ab initio” method? Bob Parr of UNC-CH in 1950s; See Int. J. Quantum Chem. 37(4), 327(1990) for details. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Three Approximations Born-Oppenheimer approximation Electrons act separately of nuclei, electron and nuclear coordinates are independent of each other, and thus simplifying the Schrödinger equation Independent particle approximation Electrons experience the ‘field’ of all other electrons as a group, not individually Give birth to the concept of “orbital”, e.g., AO, MO, etc. LCAO-MO approximation Molecular orbitals (MO) can be constructed as linear combinations of atom orbitals, to form Slater determinants 10/1/2007 Introduction to Computational Chemistry

Born-Oppenheimer Approximation
10/1/2007 Born-Oppenheimer Approximation the nuclei are much heavier than the electrons and move more slowly than the electrons freeze the nuclear positions (nuclear kinetic energy is zero in the electronic Hamiltonian) calculate the electronic wave function and energy E depends on the nuclear positions through the nuclear-electron attraction and nuclear-nuclear repulsion terms E = 0 corresponds to all particles at infinite separation 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Approximate Wavefunctions
10/1/2007 Approximate Wavefunctions Construction of one-electron functions (molecular orbitals, MO’s) as linear combinations of one-electron atomic basis functions (AOs)  MO-LCAO approach. Construction of N-electron wavefunction as linear combination of anti-symmetrized products of MOs (these anti-symmetrized products are denoted as Slater-determinants). Except for the one-electron case, the time-independent Schrödinger equation cannot be solved explicitly and exactly. So applications are needed for many-electron atoms and molecules. Notice that Hamiltonian can always be explicitly obtained for any system, so approximations come in for the total electron wavefunction. The first well-known approximation is the molecular orbital, which is indeed an one-electron wavefunction approximated by the linear combination of atomic orbitals (LCAO). To built an approximate N-electron total wavefunction, we start from a set of MOs, form products, and then anti-symmetrize them as required by the fact that electrons are fermions. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

The Slater Determinant
10/1/2007 The Slater Determinant One way, if not the ONLY way, to form such an anti-symmetrized MO products is the Slater determinant, with which everyone knows that if one row or column permutates with another, the sign of the determinant is changed. This is the reason why this kind of determinant is anti-symmetrized. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 The Two Extreme Cases One determinant: The Hartree–Fock method. All possible determinants: The full CI method. There are N MOs and each MO is a linear combination of N AOs. Thus, there are nN coefficients ukl, which are determined by making stationary the functional: The ij are Lagrangian multipliers. With the Slater determinant as the building block to approximate the total electron wavefunction, many approximate levels of theory/computation can be derived. There are two extreme cases, one with only one Slater determinant and the other with as many Slater determinants as possible (as a linear combination). We call the first (simplest theory level) the Hartree-Fock method, and the second the Full Configuration Interaction (Full CI, or FCI in short) method. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 The Full CI Method The full configuration interaction (full CI) method expands the wavefunction in terms of all possible Slater determinants: There are possible ways to choose n molecular orbitals from a set of 2N basis functions. The number of determinants gets easily much too large. For example: Let’s talk about the most complicated case first. In the Full CI method, the total N-electron wave function is approximated/expanded by a combination of all possible determinants. For Davidson’s method can be used to find one or a few eigenvalues of a matrix of rank 109. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

The Hartree–Fock Method
10/1/2007 The Hartree–Fock Method The other extreme case is where one only works work one 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 equations 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

The Hartree–Fock Method
10/1/2007 The Hartree–Fock Method Overlap integral Density Matrix The resultant solution is then a matrix equation, called Hartree-Fock-Roothaan Equation, with the overlap, density and Fock matrices defined explicitly in terms of the atomic basis space. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Self-Consistent-Field (SCF)
10/1/2007 Self-Consistent-Field (SCF) 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. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Ab Initio Methods Full CI Hartree-Fock (HF-SCF) Semi-empirical methods
10/1/2007 Ab Initio Methods Semi-empirical methods (MNDO, AM1, PM3, etc.) Hartree-Fock (HF-SCF) excitation hierarchy (CIS,CISD,CISDT,...) (CCS, CCSD, CCSDT,...) perturbational hierarchy (MP2, MP3, MP4, …) excitation hierarchy (MR-CISD) perturbational hierarchy (CASPT2, CASPT3) Here is the diagram to visually illustrates all ab initio methods and the relationship among them. Sitting in the middle is the Hartree-Fock method, and at the bottom is the Full CI method. There exists two ways to go from H-F method to FCI, one via perturbation theories such as MPn and CASPTn, and the other via variational approaches like CI, MCSCF, CASSCF, etc. Notice that I also listed semi-empirical approaches here because they are also based on the single Slater determinant with the minimum basis set. Multiconfigurational HF (MCSCF, CASSCF) Full CI 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Who’s Who 10/1/2007 Here are the most prominent people who have contributed to the development of both quantum mechanical ab initio and density functional methods. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Size vs Accuracy Number of atoms 0.1 1 10 100 1000 Accuracy (kcal/mol)
10/1/2007 Size vs Accuracy Number of atoms 0.1 1 10 100 1000 Accuracy (kcal/mol) Coupled-cluster, Multireference Nonlocal density functional, Perturbation theory Local density functional, Hartree-Fock Semiempirical Methods Full CI This plot shows the correlation, given the present available computing capacity, between the system size and the obtained result accuracy. Shown on the curves are the available computational approaches for the particular system size and corresponding accuracy. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Equilibrium structure of (H2O)2 W.K., J.G.C.M. van Duijneveldt-van de Rijdt, and F.B. van Duijneveldt, Phys. Chem. Chem. Phys. 2, 2227 (2000). 95.7 pm 96.4 pm 95.8 pm ROO,e= pm symmetry: Cs Experimental [J.A. Odutola and T.R. Dyke, J. Chem. Phys 72, 5062 (1980)]:  ROO2 ½ = ± 0.4 pm SAPT-5s potential [E.M. Mas et al., J. Chem. Phys. 113, 6687 (2000)]:  ROO2 ½ – ROO,e= 6.3 pm  ROO,e(exptl.) = pm Here is an example. For small systems of this size, only two water molecules, water dimer, the theoretical result accuracy can be very good, comparable to what one can obtain from experiments. In this particular case, theoretical prediction of O-O distance is A, whereas experimentally it is 2.913A. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Experimental and Computed Enthalpy Changes He in kJ/mol
10/1/2007 Experimental and Computed Enthalpy Changes He in kJ/mol This table shows another aspect of theoretical prediction, on reaction enthalpy of typical small molecule reactions. Theoretical results, especially those from the CCSD(T) method, agree very well with experimental data. Gaussian-2 (G2) method of Pople and co-workers is a combination of MP2 and QCISD(T) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 LCAO  Basis Functions ’s are called basis functions usually centered on atoms can be more general and more flexible than atomic orbitals larger number of well chosen basis functions yields more accurate approximations to the molecular orbitals 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Basis Functions Slaters (STO) Gaussians (GTO) Angular part * Better basis than Gaussians 2-electron integrals hard 2-electron integrals simpler Wrong behavior at nucleus Decrease to fast with r To build approximate molecular orbitals for the Slater determinant via the so-called LCAO (linear combination of atomic orbitals) scheme, we need to know atomic orbitals. This is the place we now know where the concept of basis sets comes in, where one knows predefined basis functions to represent atomic orbitals. Two basic categories of basis functions are available, STO (Slater-type orbital) and GTO (Gaussian-type orbital). The advantage of STO is its better behavior in approximate real electrons, especially in the long range but it’s computationally very costly, whereas for GTO, though not very good in describing electron at nuclei cusps and at the long range, it is more computationally efficient. This is why GTO has been the choice for most of ab initio calculations. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Contracted Gaussian Basis Set
10/1/2007 Contracted Gaussian Basis Set Minimal STO-nG Split Valence: 3-21G,4-31G, 6-31G Each atom optimized STO is fit with n GTO’s Minimum number of AO’s needed Contracted GTO’s optimized per atom Doubling of the number of valence AO’s A compromise is in the following scenario: an atomic orbital is still represented by an STO, but then the STO is expanded by a set of GTOs. Two such popular examples is the so-called minimum basis set, STO-nG, where one STO is expanded by n GTO functions, and the split-valence basis set, such as 6-31G, where for inner shells atomic orbitals are expanded with n=6 GTOs, but for the outer valence shell each atomic orbital is represented by two (splitted) sets of GTOs, one expanded by 3 GTOs and the other by only one GTO. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Polarization / Diffuse Functions
10/1/2007 Polarization / Diffuse Functions Polarization: Add AO with higher angular momentum (L) to give more flexibility Example: 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: G** Two kinds of functions can be added/appended to the standard basis set, polarization and diffusion. A polarization function, denoted by * (added to non-H elements) or **(added to both non-H and H, and thus all elements), adds AOs with higher angular momentum to give more flexibility for a basis set. A diffusion function, represented by + (added to for non-H elements) and ++ (to all elements), adds AOs with very small exponents so that they decay very slowly. This latter function is important for such systems as anions and excited states. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Correlation-Consistent Basis Functions
10/1/2007 Correlation-Consistent Basis Functions 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) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Pseudopotentials, Effective Core Potentials
10/1/2007 Pseudopotentials, Effective Core Potentials 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 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Correlation Energy HF does not include correlations anti-parallel electrons Eexact – EHF = Ecorrelation Post HF Methods: Configuration Interaction (CI, MCSCF, CCSD) Møller-Plesset Perturbation series (MP2, MP4) Density Functional Theory (DFT) Electron correlation has two kinds, static (Fermi, parallel-spin, exchange) and dynamic (Columbic, anti-parallel spin). The static electron correlation is accounted for by the exchange interaction between parallel-spin electrons, whereas for the dynamic correlation effect, post-Hartree-Fock methods have to be employed. The conventional way of defining the dynamic electron correlation energy is the difference between the “exact” energy of the system and its Hartree-Fock limit energy. In ab initio theory, two approaches are available to calculate the correlation energy, one via configuration interaction and the other through perturbation theory. Of course, one can also get it in the density functional theory. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Configuration-Interaction (CI)
10/1/2007 Configuration-Interaction (CI) In Hartree-Fock theory, the n-electron wavefunction is approximated by one single Slater-determinant, denoted as: This determinant is built from n orthonormal spin-orbitals. The spin-orbitals that form are said to be occupied. The other orthonormal spin-orbitals that follow from the Hartree-Fock calculation in a given one-electron basis set of atomic orbitals (AOs) are known as virtual orbitals. For simplicity, we assume that all spin-orbitals are real. In electron-correlation or post-Hartree-Fock methods, the wavefunction is expanded in a many-electron basis set that consists of many determinants. Sometimes, we only use a few determinants, and sometimes, we use millions of them: In this notation, is a Slater determinant that is obtained by replacing a certain number of occupied orbitals by virtual ones. Three questions: 1. Which determinants should we include? 2. How do we determine the expansion coefficients? 3. How do we evaluate the energy (or other properties)? To correctly describe the instantaneous interaction of electrons, the inter-electron distance must be introduced. The most conceptually simple way of achieving this is via Configuration Interaction (CI). CI uses a wavefunction which is a linear combination of the HF determinant and determinants from excitations of electrons. In the CI method, more than one Slater determinant are used to approximate the total electron wave function and uses the Hartree-Fock theory as its reference. In front of each of the extra configurations (determinants), there is an associated coefficient to measure the extent/importance of the extra configuration. These extra determinants are obtained from exciting one or more electrons form the ground-state Hartree-Fock configuration. So in principle there could be millions or even billions of ways to compose additional Slater determinants. Following three questions remain: which determinants should be included; how to determine the coefficients, and to how to calculate the total electron energy and other properties. The CI expansion is variational and, if the expansion is complete (Full CI), gives the exact correlation energy (within the basis set approximation). The number of determinants in Full CI grows exponentially with the system size, making the method impractical for all but the smallest systems. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Truncated configuration interaction: CIS, CISD, CISDT, etc.
10/1/2007 Truncated configuration interaction: CIS, CISD, CISDT, etc. We start with a reference wavefunction, for example the Hartree-Fock determinant. We then select determinants for the wavefunction expansion by substituting orbitals of the reference determinant by orbitals that are not occupied in the reference state (virtual orbitals). Singles (S) indicate that 1 orbital is replaced, doubles (D) indicate 2 replacements, triples (T) indicate 3 replacements, etc. Since it’s impossible to include all possible determinants in the CI method, we need develop schemes to have truncated CI methods, that is, only a limited number of determinants are included. Here are some ways: start from the Hartree-Fock reference determinant, then excite 1 electron from the occupied orbital to a virtual (unoccupied) orbital to compose a CI approached called CIS (that is, electrons are singly excited). There are many possibilities that one electron can be excited from an occupied orbital. All these possibilities are combined together to form the set of determinants for the CIS method. Next, we allow both 1 and 2 electrons to be simultaneously excited to coin the CISD method, in which linear combination of all possible singly and doubly excited configurations (determinants) forms the approximation for the total wave function. Again, if we allow singly, doubly and triply excited states in the theory, then we can the CISDT approach. Brillouin's Theorem states that singly excited determinants do not mix with the HF determinant. Therefore CISD is the cheapest worthwhile form of CI, yet this method scales as O(N6) where N is the size of the system. The other main problem with truncated CI is that it is not size consistent. For CISD, an approximate way to correct for these effects is to introduce the Davidson correction. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Truncated Configuration Interaction
10/1/2007 Truncated Configuration Interaction Number of linear variational parameters in truncated CI for n = 10 and 2N = 40. This slide shows how large the number of different levels of configurations can be. Say, the system has 10 electrons and a total of 40 basis functions, the total number of single excitation is 300. So at the level of CIS, a total of 300 configurations will be included in the linear combination. At the next level, CISD, the number goes up to 78,600 and at CISDT level, the total number of possible configurations is 18 million. If all possible excitation is considered, that is, at the FCI level, the number is about 1 billion! 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Multi-Configuration Self-Consistent Field (MCSCF)
10/1/2007 Multi-Configuration Self-Consistent Field (MCSCF) The MCSCF wavefunctions consists of a few selected determinants or CSFs. In the MCSCF method, not only the linear weights of the determinants are variationally optimized, but also the orbital coefficients. One important selection is governed by the full CI space spanned by a number of prescribed active orbitals (complete active space, CAS). This is the CASSCF method. The CASSCF wavefunction contains all determinants that can be constructed from a given set of orbitals with the constraint that some specified pairs of - and -spin-orbitals must occur in all determinants (these are the inactive doubly occupied spatial orbitals). Multireference CI wavefunctions are obtained by applying the excitation operators to the individual CSFs or determinants of the MCSCF (or CASSCF) reference wave function. A different strategy is used for the multi-configuration self-consistent-field (MCSCF) method where not only the linear weights of the determinants are variationally optimized, but also the orbital coefficients of each molecular orbital. Two other methods, CASSCF and MRCI are also available. Internally-contracted MRCI: 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Coupled-Cluster Theory
10/1/2007 Coupled-Cluster Theory System of equations is solved iteratively (the convergence is accelerated by utilizing Pulay’s method, “direct inversion in the iterative subspace”, DIIS). CCSDT model is very expensive in terms of computer resources. Approximations are introduced for the triples: CCSD(T), CCSD[T], CCSD-T. Brueckner coupled-cluster (e.g., BCCD) methods use Brueckner orbitals that are optimized such that singles don’t contribute. By omitting some of the CCSD terms, the quadratic CI method (e.g., QCISD) is obtained. The theoretical framework of Coupled Cluster (CC) theory was developed in the late 1960s, but it was not until the late 1970s that the practical implementation began to take place and until 1982 that the corner stone of modern implementation, CCSD (CC including all single and double excitations), was presented. CC solves the size consistency problem of CI by forming a wave function where the excitation operators are exponentiated. The advantage of CC theory is that higher excitations are partially included, but their coefficients are determined by the lower order excitations. With a large enough basis set CCSD typically recovers 95% of the correlation energy for a molecule at equilibrium geometry, while CCSD(T) sees a further five- to ten-fold reduction in error. With such accuracy CC has become the method of choice for accurate small-molecule calculations, even though the method is not variational (property 6, above). A method closely related to CCSD is Brueckner Doubles (BD), which uses the Brueckner orbitals rather than the HF orbitals for a CCSD treatment. The Brueckner orbitals are defined as the set of orbitals for which the single excitation coefficients are zero. Finding these orbitals makes the theory slightly more computationally intensive (BD and BD(T) still scale as O(N6) and O(N7) respectively). However, BD theory promises a slight increase in accuracy above CCSD. A more acceptable way to make truncated CI size consistent was introduced by Pople et al. in Termed Quadratic Configuration Interaction (QCISD), it is formed by the addition of higher excitation terms, quadratic in the expansion coefficients, which force size-consistency. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Møller-Plesset Perturbation Theory
10/1/2007 Møller-Plesset Perturbation Theory The Hartree-Fock function is an eigenfunction of the n-electron operator . We apply perturbation theory as usual after decomposing the Hamiltonian into two parts: More complicated with more than one reference determinant (e.g., MR-PT, CASPT2, CASPT3, …) MP2, MP3, MP4, …etc. number denotes order to which energy is computed (2n+1 rule) Møller-Plesset Perturbation theory treats the exact Hamiltonian as a small perturbation from the HF Hamiltonian -- the sum of the one-electron Fock operators. The solution of the perturbed equation to zero or first order (n = 1) gives the unperturbed Hartree-Fock energy and wave function. Second (MP2), third (MP3), and fourth (MP4) order Møller-Plesset calculations are standard levels used in calculating small systems and are implemented in many computational chemistry codes. Higher level MP level calculations are possible in some code, however, they are rarely used. The MPn energies are size consistent, but not variational. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Semi-empirical molecular orbital methods
10/1/2007 Semi-empirical molecular orbital methods Approximate description of valence electrons Obtained by solving a simplified form of the Schrödinger equation Many integrals approximated using empirical expressions with various parameters Semi-quantitative description of electronic distribution, molecular structure, properties and relative energies Cheaper than ab initio electronic structure methods, but not as accurate 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Semi-Empirical Methods
10/1/2007 Semi-Empirical Methods These methods are derived from the Hartee–Fock model, that is, they are MO-LCAO methods. They only consider the valence electrons. A minimal basis set is used for the valence shell. Integrals are restricted to one- and two-center integrals and subsequently parametrized by adjusting the computed results to experimental data. Very efficient computational tools, which can yield fast quantitative estimates for a number of properties. Can be used for establishing trends in classes of related molecules, and for scanning a computational poblem before proceeding with high-level treatments. A not of elements, especially transition metals, have not be parametrized Semiempirical Methods are simplified versions of Hartree-Fock theory using empirical (=derived from experimental data) corrections in order to improve performance. These methods are usually referred to through acronyms encoding some of the underlying theoretical assumptions. The most frequently used methods (MNDO, AM1, PM3) are all based on the Neglect of Differential Diatomic Overlap (NDDO) integral approximation, while older methods use simpler integral schemes such as CNDO and INDO. All three approaches belong to the class of Zero Differential Overlap (ZDO) methods, in which all two-electron integrals involving two-center charge distributions are neglected. A number of additional approximations are made to speed up calculations (see below) and a number of prameterized corrections are made in order to correct for the approximate quantum mechanical model. How the parameterization is performed characterizes the particular semiempirical method. For MNDO, AM1, and PM3 the parameterization is performed such that the calculated energies are expressed as heats of formations instead of total energies. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Semi-Empirical Methods
10/1/2007 Semi-Empirical Methods Number 2-electron integrals (mu|ls) is n4/8, n = number of basis functions Treat only valence electrons explicit Neglect large number of 2-electron integrals Replace others by empirical parameters Models: Complete Neglect of Differential Overlap (CNDO) Intermediate Neglect of Differential Overlap (INDO/MINDO) Neglect of Diatomic Differential Overlap (NDDO/MNDO, AM1, PM3) MNDO, PM3, and AM1 are representatives of the NDDO (neglect of diatomic differential overlap) family of methods. As this model is applied to AM1 and PM3, there are seven basic parameters that must be considered for each atom. These are augmented with up to three (four in the special case of carbon) Gaussian corrections to adjust the core/core repulsion function (CRF). The two parameters with the largest effect are the one-center/one-electron energies, Uss and Upp. These represent the kinetic energy and core-electron attractive energy of single electrons in s- and p-orbitals. The next pair of parameters are adjustments to the two-center/one-electron resonance integral, βμν, and are termed βs and βp. These parameters are responsible for bonding interactions between atoms. Another approximation within AM1 is the use of Slater functions to describe spatial features of the atomic orbitals. Slater functions are used because they require fewer parameters and are more easily parameterized. The exponents of the s- and p-orbitals on each atom become parameters and are abbreviated respectively, ζs and ζp. It should be noted that ζs and ζp also affect βμν, as it is proportional to the overlap integral (Sμν), which is in turn calculated from the Slater exponents. MNDO differs from AM1 and PM3 in that, for the lighter elements near the top of the Periodic Table, the following assumptions were made to save time:ζs = ζp and βs = βp. Also, the MNDO method includes no Gaussian functions. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Approximations of 1-e integrals
10/1/2007 Approximations of 1-e integrals Umm from atomic spectra VAB value per atom pair m,u on the same atom Continuing with the neglect of differential overlap, all two-electron integrals involving charge clouds arising from the overlap of two atomic orbitals on different centers are ignored. All overlap integrals arising from the overlap of two different atomic orbitals are neglected. The MNDO, AM1, and MNDO-d one-center two-electron integrals are derived from experimental data on isolated atoms. For each atom there are a maximum of five one-center two-electron integrals. One b parameter per element 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Popular DFT Noble prize in Chemistry, 1998 In 1999, 3 of top 5 most cited journal articles in chemistry (1st, 2nd, & 4th) In , top 3 most cited journal articles in chemistry In 2005, 4 of top 5 most cited journal articles in chemistry 1st, Becke’s hybrid exchange functional (1993) 2nd, Lee-Yang-Parr correlation functional (1988) 3rd, Becke’s exchange functional (1988) 5th, PBE correlation functional (1996) 10/1/2007 Introduction to Computational Chemistry

Advantageous DFT Computationally efficient Hartree-Fock-like computationally (~N3) , but included electron correlation effects Theoretically rigorous Two Hohenberg-Kohn theorems guarantee an exact theory in ground state Conceptually insightful Provides basis to understand chemical reactivity and other chemical properties 10/1/2007 Introduction to Computational Chemistry

Brief History of DFT First speculated 1920’ Thomas-Fermi (kinetic energy) and Dirac (exchange energy) formulas Officially born in 1964 with Hohenberg- Kohn’s original proof GEA/GGA formulas available later 1980’ Becoming popular later 1990’ Pinnacled in 1998 with a chemistry Nobel prize 10/1/2007 Introduction to Computational Chemistry

What could expect from DFT?
LDA, ~20 kcal/mol error in energy GGA, ~3-5 kcal/mol error in energy G2/G3 level, some systems, ~1kcal/mol Good at structure, spectra, & other properties predictions Poor in H-containing systems, TS, spin, excited states, etc. 10/1/2007 Introduction to Computational Chemistry

Density Functional Theory
Hohenberg-Kohn theorems: “Given the external potential, we know the ground-state energy of the molecule when we know the electron density ”. The energy density functional is variational. 10/1/2007 Introduction to Computational Chemistry

Can we work with E[]? How do we compute the energy if the density is known? The Coulombic interactions are easy to compute: But what about the kinetic energy TS[] and exchange-correlation energy Exc[]? How do we determine the density variationally? We must make sure that the density is derived from a proper N-electron wavefunction (N-representability problem) and a given external potential vext (v-representability problem). 10/1/2007 Introduction to Computational Chemistry

The Kohn-Sham (KS) Scheme
Suppose, we know the exact density. Then, we can formulate a Slater determinant that generates this exact density (= Slater determinant of system of N non-interacting electrons with same density ). We know how to compute the kinetic energy from a Slater determinant. The N-representability problem will then be solved (density is obtained from an anti-symmetric N-electron function). Then, the only thing unknown is to calculate Exc[]. 10/1/2007 Introduction to Computational Chemistry

10/1/2007 Kohn-Sham Equations The Only Unknown Add nice image of something interesting; A view graph emphasizing that we must make approximations In DFT, everything we don’t know is grouped under the term “Exchange-correlation energy” (Feyman: the “stupid” energy). We know how to get it exactly for very simple systems– these solutions are then applied to more complex systems; we get good results which agree well with experiment. A jpg model of a protein folding or an animation of protein folding Communicate that DFT is very important; this is the most significant work in science 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

All about Exchange-Correlation Energy Density Functional
LDA – f is a function of (r) only GGA – f is a function of (r) and ∇(r) Mega-GGA – f is also a function of ts(r), kinetic energy density Hybrid – f is GGA functional with extra contribution from Hartree-Fock exchange energy 10/1/2007 Introduction to Computational Chemistry

LDA Functionals Thomas-Fermi formula (Kinetic) – 1 parameter Slater form (exchange) – 1 parameter Wigner correlation – 2 parameters 10/1/2007 Introduction to Computational Chemistry

GGA Functional: BLYP Two most well-known functionals are the Becke exchange functional Ex[] with 2 extra parameters &  the Lee-Yang-Parr correlation functional Ec[] with 4 parameters a-d Together, they constitute the BLYP functional: 10/1/2007 Introduction to Computational Chemistry

Hybrid Functional: B3LYP
FxB and FcLYP have been fitted against ab initio data (one could call this computational approach a “semi-ab-initio method”). In a very popular variant, denoted B3LYP, the functional is augmented with a little of Hartree-Fock-type exchange: 10/1/2007 Introduction to Computational Chemistry

Other Popular Functionals
LDA SVWN GGA PBE PW91 HCTH Mega-GGA Hybrid functionals 10/1/2007 Introduction to Computational Chemistry

Disadvantageous DFT ground-state theory only universal functional unknown no systematic way to improve approximations like LDA, GGA, etc. 10/1/2007 Introduction to Computational Chemistry

Examples DFT vs. HF Hydrogen molecules - using the LSDA (LDA)
10/1/2007 Examples DFT vs. HF Here is an example of how different the performance of DFT and HF methods will be in reproducing the accurate potential energy surface. Here the hydrogen molecule, H2, is used as the example. Hydrogen molecules - using the LSDA (LDA) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

DFT Reactivity Indices
10/1/2007 DFT Reactivity Indices Electronegativity (chemical potential) Hardness / Softness HSAB Principle and Maximum Hardness Principle DFT concepts and reactivity indices are an integral part of DFT in chemistry, which could be used to understand molecular reactivity, stability and so like. Two widely used chemical concepts that found a theoretical ground in DFT are electronegativity and chemical/global hardness, which can be defined as the first and second derivative of the total electronic energy with respect to the total electron number with the external potential from the nuclei fixed. FOR MORE INFO... Parr & Yang, Density Functional Theory of Atoms and Molecules (Oxford Univ. Press, New York, 1989). 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

DFT Concept: Fukui Function
10/1/2007 DFT Concept: Fukui Function Fukui function Nucleophilic attack Electrophilic attack A recent development was the so-called Fukui function which can be used to predict nucleophilic, electrophlic, and free-radical attacks of a molecular system. Free radical activity 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Fukui Function: An Example
10/1/2007 Fukui Function: An Example Here is an example of how difference the reactivity prediction from different electronic properties might be for the squalene molecule, where only the Fukui function gives the correct prediction. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Fukui Function: Another Example
10/1/2007 Introduction to Computational Chemistry

New Development: Electrophilicity Index
Physical meaning: suppose an electrophile is immersed in an electron sea The maximal electron flow and accompanying energy decrease are Parr, Szentpaly, Liu, J. Am. Chem. Soc. 121, 1922(1999). 10/1/2007 Introduction to Computational Chemistry

New Development: Philicty and Spin-Philicity
Philicity: defined as ·f(r) Chattaraj, Maiti, & Sarkar, J. Phys. Chem. A 107, 4973(2003) Still a very controversial concept, see JPCA 108, 4934(2004); Chattaraj, et al. JPCA, in press. Spin-Philicity: defined same as  but in spin resolution Perez, Andres, Safont, Tapia, & Contreras. J. Phys. Chem. A 106, 5353(2002) 10/1/2007 Introduction to Computational Chemistry

New Development: Steric Effect
S.B. Liu, J. Chem. Phys. 126, (2007). 10/1/2007 Introduction to Computational Chemistry

New Development: Steric Effect
BLACK CIRCLE: Total Energy Difference; RED SQUARE: Electrostatic; GREEN DIMOND: Quantum; BLUE TRIANGLE: Steric S.B. Liu and N. Govind, to be published 10/1/2007 Introduction to Computational Chemistry

10/1/2007 What’s New: QM/MM Focus: Enzyme catalytic reactions Strategy: QM for active site and MM for the rest Main Issue: boundary between QM and MM. Models: Link-atom, pseudo-orbital, pseudo-bond, etc. Limitation: active site should be small; long-range charge transfer conformation change (protein folding) Quantum chemical methods are generally applicable and allow the calculation of ground and excited state properties (molecular energies and structures, energies and structures of transition states, atomic charges, reaction pathways etc.). Molecular Mechanical methods are restricted to the classes of molecule it have been designed for and their success strongly depends on the careful calibration of a large number of parameters. The development of the hybrid QM/MM approaches is guided by the general idea that large chemical systems may be partitioned into an electronically important region which requires a quantum chemical treatment and a remainder which only acts in a perturbative fashion and thus admits a classical description. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

QM/MM Example: Triosephosphate Isomerase (TIM)
10/1/2007 QM/MM Example: Triosephosphate Isomerase (TIM) DHAP H2O Triosephosphate isomerase (TIM) is a dimeric enzyme that catalyzes the conversion between dihydroxyacetone phosphate (DHAP) and R-glyceraldehyde 3-phosphate (GAP), which is an important step in glycolysis (the enzymatic breakdown of carbohydrates). TIM increases the reaction rate by more than 109 times, and has thus been referred to as a “perfect” enzyme. Many experimental techniques have been used to study the enzyme, supplemented by a number of theoretical calculations, but the complex catalytic mechanisms are not yet fully understood. Three possible mechanisms for the second step of TIM-catalyzed reactions, which involves a proton transfer, have been studied by the combined quantum mechanical/molecular mechanical (QM/MM) approach at a number of QM levels. GAP 494 Residues, 4033 Atoms, PDB ID: 7TIM Function: DHAP (dihydroxyacetone phosphate) GAP (glyceraldehyde 3-phosphate) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

TIM 2-step 2-residue Mechanism
10/1/2007 TIM 2-step 2-residue Mechanism DHAP GAP Glu 165 (the catalytic base), His 95 (the proton shuttle) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

QM/MM: 1st Step of TIM Mechanism
10/1/2007 QM/MM: 1st Step of TIM Mechanism QM/MM size: 6051 atoms QM Size: 37 atoms QM: Gaussian’98 Method: HF/3-21G MM: Tinker Force field: AMBER all-atom Number of Water: 591 Model for Water: TIP3P MD details: 20x20x20 Å3 box, optimize until the RMS energy gradient less than 1.0 kcal/mol/Å. 20 psec MD. Time step 2fs. SHAKE, 300 K, short range cutoff 8 Å, long range cutoff 15 Å. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

QM/MM: Transition State
10/1/2007 QM/MM: Transition State ===================== Energy Barrier (kcal/mol) QM/MM Experiment An example of what the IRC curve will look like for a typical QM and QM/MM calculation, compared to the experimental value of the reaction barrier. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

What’s New: Linear Scaling O(N) Method
10/1/2007 What’s New: Linear Scaling O(N) Method Numerical Bottlenecks: diagonalization ~N3 orthonormalization ~N3 matrix element evaluation ~N2-N4 Computational Complexity: N log N Theoretical Basis: near-sightedness of density matrix or orbitals Strategy: sparsity of localized orbital or density matrix direct minimization with conjugate gradient Models: divide-and-conquer and variational methods Applicability: ~10,000 atoms, dynamics Algorithms for calculating properties of a large complex system of N particles are "linear scaling" if the computational effort needed to solve the desired equations is proportional to the total size of the system, i.e., "Order N". This is true in classical mechanics: if all forces are short range, then the basic equations can be solved in time proportional to the number of particles. For example, this could be one time step of a molecular dynamics simulation. (Long range Coulomb forces can also be handled.) However, quantum mechanics is intrinsically not linear scaling. The solutions of the wave equation in general depend upon the boundary conditions. Each eigenstates of an extended periodic system is delocalized and its values everywhere depends upon the boundary conditions. Sharp band edges, critical pints in the band structure, a sharp Fermi surface in k space, Kohn anomalies, ... all require extended quantum mechanical waves. Thus in general the wave nature of quantum mechanics leads to non-locality. In many-body systems exact solutions grow exponentially with the number of particles N, and practical approximate forms often scale as high powers of N. For non-interacting fermion systems the Pauli exclusion principle requires there to be N eigenstates, each extended, i.e., of size proportional to N, and each required to be orthogonal to each of the N other eigenstates, leading to effort scaling as N3. This is the scaling of the current efficient plane wave calculations we have described before. (The scaling can be reduced to N2 by using localized bases and other tricks.). 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

O(N) Method: An Example
10/1/2007 O(N) Method: An Example OLMO NOLMO Diagonalization Thus the fundamental question is: Under what conditions, and with what approximations can we make algorithms that are linear scaling? Key papers for the basic understanding are ones by Kohn, "The nature of the insulating state"; a general conceptual article by Volker Heine and a recent paper by Kohn that invokes the concept of "nearsightedness" in quantum mechanics. The second question is: In cases where linear scaling is possible, how can it be done most efficiently? This has been addressed in a series of recent papers given below that derive different methods. There is also a recent review to be published in Rev Mod Phys by S. Goedecker. The key steps in the solution are to recognize that integrated quantities like the total energy and forces depend only upon the density or the density matrix - eigenstates are not required. For these functions one can make unitary transformations of the occupied eigenstates to define localized states with the same density, total energy, etc. These are Wannier like functions. Each function is defined by equations local to a given region. In insulators the functions are exponentially localized, which defines the localization rigorously. The most general approach is in terms of the density matrix, which is exponentially localized in an insulator or in a metal at non-zero temperature. Expressed in a finite basis, the density matrix becomes a sparse matrix that can be treated in an order N manner. In addition, one can introduce Green's function and projection methods that explicitly project out the ground state (formally related to the method used for projecting the ground state in quantum Monte Carlo simulations.) 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 What Else … ? Solvent effect Implicit model vs. explicit model Relativity effect Transition state Excited states Temperature and pressure Solid states (periodic boundary condition) Dynamics (time-dependent) A few other topics are not covered here and will be addressed elsewhere. They include implicit and explicit solvent models, relativity effect, transition state theory, temperature and pressure, periodic boundary condition and dynamics. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

Limitations and Strengths of ab initio quantum chemistry
10/1/2007 Limitations and Strengths of ab initio quantum chemistry This slide summarizes the advantage and disadvantage of quantum mechanic (ab initio and DFT) methods. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Popular QM codes Gaussian (Ab Initio, Semi-empirical, DFT) Gamess-US/UK (Ab Initio, DFT) Spartan (Ab Initio, Semi-empirical, DFT) NWChem (Ab Initio, DFT, MD, QM/MM) MOPAC/2000 (Semi-Empirical) DMol3/CASTEP (DFT) Molpro (Ab initio) ADF (DFT) ORCA (DFT) Thuis slide gives you a rough idea what free and commercial software are available nowadays for the quantum mechanical calculations. 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

10/1/2007 Reference Books Computational Chemistry (Oxford Chemistry Primer) G. H. Grant and W. G. Richards (Oxford University Press) Molecular Modeling – Principles and Applications, A. R. Leach (Addison Wesley Longman) Introduction to Computational Chemistry, F. Jensen (Wiley) Essentials of Computational Chemistry – Theories and Models, C. J. Cramer (Wiley) Exploring Chemistry with Electronic Structure Methods, J. B. Foresman and A. Frisch (Gaussian Inc.) Pass around copies of the texts We can get the book store to order some if there is enough demand Most will need to buy Exploring Chemistry – we need to order that directly from Gaussian 10/1/2007 Introduction to Computational Chemistry Renaissance Computing Institute, UNC-CH

QUESTIONS & COMMENTS? Please direct comments/questions about Comp Chem to Please direct comments/questions pertaining to this presentation to 10/1/2007 Introduction to Computational Chemistry

Hands-on: Part I Purpose: to get to know the available ab initio and semi-empirical methods in the Gaussian 03 / GaussView package ab initio methods Hartree-Fock MP2 CCSD Semiempirical methods AM1 10/1/2007 Introduction to Computational Chemistry

Hands-on: Part II Purpose: To use LDA and GGA DFT methods to calculate IR/Raman spectra in vacuum and in solvent. To build QM/MM models and then use DFT methods to calculate IR/Raman spectra DFT LDA (SVWN) GGA (B3LYP) QM/MM 10/1/2007 Introduction to Computational Chemistry

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