Harry's influence on my early and recent career: What harm can't be made by integrals

Transcription

1 Harry's influence on my early and recent career: What harm can't be made by integrals Roland Lindh Dept. Quantum Chemistry The Ångström Laboratory Uppsala

2 Would you dare to buy used integrals from this man?

3 Outline ERI archeology Present use of the Rys-Gauss Quadrature Furture

4 Where to start? Harry's publication list Importance of ERIs The Björn Roos group IBM Almaden 2-electron integral technology before 1990.

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7 The Electron-repulsion integrals The bottleneck in most ab Initio methods describing the electron-electron integration.

8 The Gang of Four

9 Post Doc at IBM research Lab Enrico Clementi Doug McLean Megumu Yoshimine Bowen Liu Bill Lester Paul Bagus - MCSCF theory - The ATOM-SCF program

10 Integrals methods: Incomplete gamma functions Boys (1950) Jan Almlöf, the Molecule program (1972) The Pople-Hehre method (1978) The McMuchie-Davidson method (1978) The Obara-Saika method (1986) The HGP method (VRR & HRR) (1988) and more...

11 Key developments The computation of integrals in sets of angular shells Improved computer languages and compilers

12 Pople-Hehre (1978) Simplification by use of internal symmetry for Lshell basis sets.

13 McMuchie-Davidson (1978) Use of Hermite Cartesians as intermediates. Bra and ket representations can be manipulated independently.

14 Obara-Saika (1986)

15 HGP (1988)

16 HGP (1988)

17 HGP (1988)

18 HGP (1988) Vertical Recurrence Relation (VRR):

19 HGP (1988) Vertical Recurrence Relation (VRR): Horizontal Recurrence Relation (HRR):

20 HGP (1988) Vertical Recurrence Relation (VRR): Horizontal Recurrence Relation (HRR):

21 Rys-Guass Quadrature - an exact quadrature based on the roots and weights of the Rys-Gauss orthonormal polynomials - recurrence relations based on the properties of the integrand rather than the integral. - The important intermediates are the so-called 2D-integrals - robust and suited for computer implementation

22 Rys-Gauss quadrature Notes on the first implementation HONDO program package Superior performance for high angular momentum Simple extension to higher order derivatives

23 My Post IBM Almaden I did my post doc under the supervision of Dr. Bowen Liu. Part of my job was to enable Guassian 88 for the IBM mainframes. Desperate for a challanging software project I suggested that I would write an integrals code. Bowen said OK! Desperate plans require bold goals!

24 1989: yet another integral code To develop a new integral method and implementation to replace MOLECULE. Specs Novel method (publishable work) Improved and maintainable computer code General contraction (partitioning technique) Real Spherical Harmonics (on-the-fly) Double-coset symmetry adaptation Improved performance for low angular mom. A new method is a hybrid of the modern Incomplete Gamma function based methods and the best parts of the Rys-Gauss Quadrature.

25 But there was a little problem! Dear Roland, a project on two-electron integrals will be the end to your academic carreer. Stay out of it!

26 But there was a little problem!

27 But there was a little problem!

28 The LRL method Faster for real spherical harmonics as compared to Cartesians One single algorithm for any degree of contraction and angular momentum Demonstrate explicitly that Rys-Gauss quadrature and Incomple Gamma function based methods are connected analytically LRL performance is still the benchmark to beat.

29 The LRL method: the roots and weights The benchmark to proceed was: Could I write a code that produce the roots and weights of the Rys-Gauss orthonormal polynomials?

30 The LRL method: the roots and weights The benchmark to proceed was: Could I write a code that produce the roots and weights of the Rys-Gauss orthonormal polynomials?

31 The LRL method The so-called 2D-integrals are manipulated with 3terms recurrence relations (cf. The 5-terms VRR).

32 The LRL method: The reduced multiplication scheme For low angular momentum (s,p) most of the entried in the general quadrature equation are redundant.

33 The LRL method By optimizing the order of the operations: Contraction HRR: bra HRR: ket Cartesian Real Sperical Harmonics: bra Cartesian Real Sperical Harmonics: ket Optimal performance is achieved.

34 Seward's folly 1991

35 Seward, Alaska

36 Seward, Alaska & Mckinley

37 Seward, Alaska & Mckinley

38 Present developments The Rys-Gauss quadrature is today the work horse in our development of: RI methods On-the-fly generation of auxiliary basis sets Cholesky decomposition methods for twoelectron integrals Parallelization of CD methods

39 Future The Rys-Gauss quadrature has still not been fully exploited! Simple formulation Asymptotic behavior: connection to classical multipole moment expressions Alternative for integral estimates (CS & CO)?

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41 Would you dare to buy used integrals from this man?

42 Would you dare to buy used integrals from this man? MOST DEFINETELY!

43 Summery So what are the influences of HF? I got too much involved in integrals in my early carreer Since May 1st 2010 Professor in Quantum Uppsala University Conclution: In healthy proportions integrals can be good for your acedemic carreer. Don't spend time devloping a new algorithm, waste your time on figuring out how not not have to compute them in the first place.

44 Thanks for you attention! Many thanks to Harry for inspiring a young scientist to think twice and not spoil his academic career. My sincere congratulations on your 80th birthday! Ha den äran!

45 An invitation to contribute to A Celebration of the Scientific Achievements of Björn Roos A special volume of the Guest Editors: Mike Robb, Luis Serrano-Andrés Per Siegbahn and Roland Lindh Editorial Advisory Board: Mark S. Gordon Trygve Helgaker Kimihiko Hirao Jean P. Malrieu Jeppe Olsen Kristin Pierloot Peter Pulay Klaus Ruedenberg Isaiah Shavitt Hans-Joachim Werner Under the auspices of