MSc in High Performance Computing Computational Chemistry Module Introduction to the Course Paul Sherwood CCLRC Daresbury Laboratory

MSc in High Performance Computing ● The course provides an overview of modern quantum and classical methods in computational chemistry, including an assessment of the accuracy and cost of the associated techniques. An overview of parallelisation strategy, focusing on the key implementation details of both quantum (NWChem and GAMESS-UK) and simulation codes (NAMD and DL-POLY) will be provided. There will be two practical sessions in which the students will have the opportunity to perform both quantum and classical simulations on HPCx. –Intended Learning Outcomes On completion of this course students should be able to: Demonstrate an understanding of the popular methods used in computational chemistry. Demonstrate an awareness of the relative costs and performance of both quantum and classical methods. Summarise the key algorithms involved in a variety of widely- used computational chemistry codes. Discuss the effectiveness of a number of parallelisation techniques employed in computational chemistry.

Course Schedule I Day 1 : Tuesday 4 th March 09:30 – 09:45Introduction to the Course (P. Sherwood) 09:45 – 10:15L1 Overview of the main techniques of computational chemistry – MD and electronic structure methods (P Sherwood) 10:15 – 11:00L2 Basic MD (W Smith) – 11.30BREAK 11:30 – 12.15L3 Parallel MD (i) (W Smith) P1 Implementing replicated data parallelism in an MD kernel 13:00 – 14:00LUNCH 14:00 – 14:45P1 Continued 14:45 – 15:30L4 Parallel MD (ii) (W Smith) 15 :30 – 16:00 L5 Characterising parallel code performance, tracing and timing analyses (P Sherwood) 16:00 16:30TEA BREAK 16:30 – 17:30P2 Performance of a distributed data MD kernel

Course Schedule II Day 2: Wednesday 5 th March 09 :30 – 10 :15P2 analysis and discussion 10:15 – 11:00 L6 Introduction to QM algorithms, underlying theory. (P Sherwood) Background material, this will not be examined – 11.30TEA BREAK 11:30 – 12:30P3 Running simple QM calculations, and interpreting the output 12:30 – 13:30LUNCH 14:00 – 14:45L7 Parallel approaches to quantum chemistry, Replicated data parallelism (Huub van Dam) 14:45 – 15:30P4 – trace a Replicated Data SCF program. 15:30 – 16:00TEA BREAK 16:00 – 17.30Free Time - option to continue practicals P1-4

Course Schedule III Day 3: Thursday 6 th March 09:30 – 10:15L8 Introducing one-sided methods and programming, Global Array Tools, compared with MPI-2 (P Sherwood) 10:15 – 11:00P5 One-sided access example using GAs - programming a matrix multiply – 11.30TEA BREAK 11:30 – 12:30P5 continued 12:30 – 13:00LUNCH 14:00 – 14:45L9 Quantum chemistry algorithms (iii), Distributed Data Algorithms (Huub van Dam) 14:45 – 15:30P6 Parallel electronic structure practical, Vampir run a distributed data SCF kernel 15:30 – 16:00BREAK 16:00 – 16:30P4,5,6 wrap up 16:30 – 17:00Question Session, Intro to Tutorial problems

MSc in High Performance Computing Computational Chemistry Module Lecture 1 - Techniques Paul Sherwood CCLRC Daresbury Laboratory

Computational methods in chemistry –molecular modelling most primitive attempting to compute of some property (often the energy) as a function of the atomic positions approaches to the computation –fundamental physics »very expensive, leading to a heirarchy of approximate methods »e.g. Hartree Fock, –paramerisations »use experiments and other computations to construct simple and efficient models –and Density Functional Theory (some parameters) –databases and cheminformatics computer is used a tools to identify –e.g. bioinformatics, search libraries for sequences –mostly integer arithmetic –often intrinsically highly parallel (divide up database or queries) –This course will concentrate on molecular modelling

The Energy and its Derivatives ● A single energy is not usually very useful… –Chemistry is controlled by energy differences ● the Potential Energy Surface (PES)

The Energy and its Derivatives –Stable chemical structures are defined by the minima of the PES differentiating the energy w.r.t the position gives us the forces on the atoms given forces, we can automatically locate minima using “geometry optimisation” techniques –Reaction enthalpies are from difference in well depths for reactants and products –At finite temperatures, more of the surface is accessible from forces (and nuclear masses) we can determine acceleration MD is the solution of the classical equations of motion by numerical methods for a system of atoms/molecules to determine the time evolution of the system Sampling can yield free energies

Properties ● Shape of potential energy surface close to the minima gives ruse to vibrational energy levels, –infra-red and raman spectra ● Some methods can also be applied to excited states –usually these have similar nuclear configuration but different electronic wavefunction –energy difference between different states can give features of UV/vis spectra ● Coupling of electron-electron and electron nuclear spins –NMR, EPR…. spectroscopy

Classical Force Field approaches ● In force fields, “molecular mechanics”, or “empirical potentials” the energy is parameterised as a function of distances, angles, dihedrals (2,3,4-body terms). ● For molecular system defined by covalent bonds, the force field can often describe distortions from the bonded structure but functional forms for bond cleavage are in their infancy. ● Expressions are very cheap to evaluate, the method of choice for macromolecular systems ● Molecular dynamics is commonly used to explore conformational space and to derive time-averages and correlation functions.

Ab-initio methods ● In contrast to the force-field based approaches, these methods are (in principle) parameter-free. ● Electrons and nuclei are included explicitly –Schroedinger’s equation can be used to find energy of stationary states ● Making and breaking of bonds can be studied –so there is no need to assume details of the chemistry ● Born Oppenheimer approximation is usually used –motion of electrons occurs on a much faster timescale that the nuclear motion (e.g. thermal vibrations), so it is reasonable to solve the electronic problem in the field of static nuclei ● Even so, full solution is very costly, and a family of approximate methods have been devised –e.g. Hartree-Fock, Moeller Plesset, Coupled Cluster... –more on this tomorrow

Semi-Empirical methods ● Similar in form to Hartree-Fock but –many terms in the energy summation are omitted –some terms are replaced with values obtained by fitting to more accurate computations, or to experiment –only valence (outer-shell) electrons get explicit treatment ● Known by Acronyms –CNDO (complete neglect of differential overlap) –MNDO (modified …...) –INDO (intermediate....) –AM1 (Austin Model 1) ● Specialised developments –large systems) MOZYME –spectroscopic properties (ZINDO)

Density Functional Theory ● Often classified as an ab-initio method, but usually there are some fitted parameters ● Based on Hohenberg-Kohn Theorem –the energy of a system of interacting particles can be obtained by solving for a hypothetical system of non-interacting particles, –This leads to a similar set of equations to those of Hartree-Fock theory except that part of the Hamiltonian (the exchange/correlation energy) is described by a Functional of the charge density –The only problem is that the correct Functional is not known, and we have to use approximate forms generated by guesswork and consideration of the correct boundary conditions –Despite not knowing the exact functional, DFT is now very widely used For reasons of cost-effectiveness it has replaced true ab-initio methods for many purposes ● Similar formalism to HF leads to strong similarities in parallelisation strategy

Classical Simulation - the CHARMM Force Field ● The value of the energy is calculated as a sum of –internal, or bonded, terms E bonded, which describe the bonds, angles and bond rotations in a molecule –a sum of external or nonbonded terms, E non-bonded, These terms account for interactions between nonbonded atoms or atoms separated by 3 or more covalent bonds.

Valence Force Fields (i) ● Used for covalently bound molecules and networks ● Terms associated with bonded groups –bonds e.g. harmonic, quartic –angles e.g. harmonic, quartic –dihedral (torsion) angles sin,cos (rotational barriers) harmonic (e..g planarity constraints) –sometimes other cross-terms bond-bond coupling bond-angle coupling

Bonded terms ● Improper Torsion (e.g. planarity constraints) ● Bonded Terms:

Non-bonded terms ● Summed over all non-covalently-bound pairs –always exclude bonded pairs –exclude 1,3 interactions for angles –sometimes scale 1,4 interactions for dihedrals ● van der Waals –Buckingham, Lennard-Jones ● electrostatics –simple coulomb (q i q j /r) Need to decide the atomic charges … –distance-dependent dielectric Approximate correction for solvation

Non-bonded Terms