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

Roland LindhDept. Quantum ChemistryThe Ångström Laboratory

Uppsala University

@

Would you dare to buy used integrals from this man?

Outline

●ERI archeology●Present use of the Rys-Gauss Quadrature●Furture

Where to start?

●Harry's publication list ●Importance of ERIs●The Björn Roos group●IBM Almaden●2-electron integral technology before 1990.

The Electron-repulsion integrals

The bottleneck in most ab Initio methods describing the electron-electron integration.

The Gang of Four

Post Doc at IBM research Lab

Enrico ClementiDoug McLeanMegumu YoshimineBowen LiuBill LesterPaul Bagus

- MCSCF theory- The ATOM-SCF program

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 ...

Key developments

●The computation of integrals in sets of angular shells●Improved computer languages and compilers

Pople-Hehre (1978)

Simplification by use of internal symmetry for L-shell basis sets.

McMuchie-Davidson (1978)

Use of Hermite Cartesians as

intermediates. Bra and ket representations can

be manipulated independently.

Obara-Saika (1986)

HGP (1988)

HGP (1988)

HGP (1988)

HGP (1988)

Vertical Recurrence Relation (VRR):Vertical Recurrence Relation (VRR):

HGP (1988)

Vertical Recurrence Relation (VRR):Vertical Recurrence Relation (VRR):

Horizontal Recurrence Relation (HRR):

HGP (1988)

Vertical Recurrence Relation (VRR):Vertical Recurrence Relation (VRR):

Horizontal Recurrence Relation (HRR):

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

Rys-Gauss quadrature

Notes on the first implementation

●HONDO program package●Superior performance for high angular momentum●Simple extension to higher order derivatives

My Post Doc @ IBM Almaden

1988-1991 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!

1989: yet another integral codeTo 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.

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!”

But there was a little problem!

But there was a little problem!

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.

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?”

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?”

The LRL method

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

The LRL method:The reduced multiplication scheme

For low angular momentum (s,p) most of the entried in the general quadrature equation are

redundant.

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.

Seward's folly

1991

Seward, Alaska

1991 1993

Seward, Alaska & Mckinley

1991 1993 1999

Seward, Alaska & Mckinley

1991 1993 1999

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 two-electron integrals●Parallelization of CD methods

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)?

Would you dare to buy used integrals from this man?

Would you dare to buy used integrals from this man?

MOST DEFINETELY!

SummerySo what are the influences of HF?

●I got too much involved in integrals in my early carreer●Since May 1st 2010 Professor in Quantum Chemistry @ 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.

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!

A Celebration of the Scientific Achievements of Björn Roos

A special volume of the Under the auspices of

An invitation to contribute to

Guest Editors: Mike Robb, Luis Serrano-Andrés Per Siegbahn and Roland LindhEditorial Advisory Board:Mark S. Gordon Trygve HelgakerKimihiko Hirao Jean P. MalrieuJeppe Olsen Kristin PierlootPeter Pulay Klaus RuedenbergIsaiah Shavitt Hans-Joachim Werner