A very high accuracy potential energy surface for H 3 Y S Mark Wu a Aron Kuppermanna and James B Andersonb a A A Noyes L aboratory of Chemical Physics Division of Chemistry and Chemical Engineering California Institute of T echnology Pasadena CA 91125 USA b Department of Chemistry T he Pennsylvania State University University Park PA 16802 USA Received 10th November 1998 Accepted 22nd December 1998 An exact quantum Monte Carlo EQMC method was used to calculate the potential energy surface PES for the ground electronic state of H over a grid of about 76 000 nuclear geometries The absolute ab initio 3 statistical or sampling error of the calculation was 0 01 kcal mol 1 for energies V smaller than 3 eV This PES was tted by a three dimensional cubic spline method and the tting accuracy was determined from a set of 3684 randomly selected nuclear geometries not used in the tting For the range V O 3 eV the rms tting error was 0 010 kcal mol 1 and the absolute value of the corresponding maximum error was 0 018 kcal mol 1 This tted EQMC PES is an order of magnitude more accurate than the best PES previously obtained for this system Detailed comparisons are made with previous PESs for the more dynamically important nuclear con gurations 1 Introduction Three ab initio tted potential energy surfaces PESs for the ground electronic state of H and its isotopomers have been 3 used in most of the calculations performed in the last decade on the quantum reaction dynamics of this system 1h16 the LSTH 17 18 DMBE 19 and BKMP220 surfaces All three have an estimated ab initio and tting accuracy of about 0 2 kcal mol 1 and give reaction cross section results that are generally in good agreement with each other justifying the label of chemically accurate for such PESs One signi cant exception to this agreement occurs however under resonance conditions Recent calculations of the di erential cross section of the reaction H D v 0 j 0 HD v 0 j D in the 2 total energy range E 1 40 1 60 eV measured with respect to the bottom of the isolated diatom well using the LSTH PES and including the e ect of the geometric phase GP have shown the existence of a pronounced backward peak for j 5 having a fwhm of 41 meV 14 A collision lifetime analysis of the scattering wave function furnished a resonance energy E 1 497 eV and a resonance lifetime of 164 fs res These calculations were repeated using the BKMP2 PES whose barrier height is 9 61 kcal mol 1 only 0 19 kcal mol 1 lower than the LSTH one The corresponding resonance energy however shifted downwards by 1 27 kcal mol 1 15 and the lifetime dropped to 52 fs showing how very sensitive the resonance characteristics are to the details of the PES Since in general the position of a pronounced peak can be determined to an energy within about 1 2 of its fwhm it is estimated that changes in the saddle point region of the order of 0 015 kcal mol 1 could a ect those characteristics in a detectable manner As a result in order to predict the resonance energy within experimental accuracy a PES with an absolute accuracy of about 0 015 kcal mol 1 in the strong interaction region is probably necessary Such a prediction is highly desirable to help guide experiments aimed at the detection of this important feature of reaction dynamics This importance derives from the high sensitivity that resonances have to the PES holding out the hope that an experimental measurement of their properties can lead to the determination of important features of the PES not achievable by other methods For these reasons we decided to calculate the PES of H 3 with an absolute accuracy of 0 01 kcal mol 1 and a tting accuracy of 0 015 kcal mol 1 over a wide region of nuclear con guration space The only method currently capable of achieving such an absolute accuracy is the exact quantum Monte Carlo EQMC method developed recently by Anderson and coworkers 21h26 This method was used by Diedrich and Anderson to calculate the H PES at 378 points with very 3 high accuracy most of them 253 for collinear con gurations This number is insufficient to span the entire threedimensional 3D surface and does not yield a 3D t accurate enough to permit the scattering calculations that were desired The results of the present extended calculations their tting and a comparison with the LSTH and BKMP2 surfaces are presented The EQMC method and the numerical parameters used are summarized in Section 2 and the design of the nuclear geometry grid and the tting procedure are described in Section 3 The results and their discussion are given in Sections 4 and 5 respectively and a summary in Section 6 2 Exact quantum Monte Carlo methodology and numerical parameters The EQMC methodology has been reviewed in some detail not too long ago 26 and only a short summary is presented here It involves a Green s function quantum Monte Carlo procedure coupled with an exact cancellation scheme for imposing the appropriate antisymmetry condition on the ground state wave function A trial wave function is selected having this antisymmetry and a number N of associated sample points the psips or walkers is selected in the 9dimensional body xed internal con guration space of the three electrons having a density proportional to the wave function All N walkers change position in con guration space according to a Monte Carlo procedure based on the property of the corresponding Green s function to reproduce the electronic wave function by an integration over con guration space 26 Local energies and their average and standard deviation are calculated by a Monte Carlo importance sampling method after each N point iteration or each block of several Phys Chem Chem Phys 1999 1 929 937 929 such iterations For each nuclear geometry the iterative procedure is interrupted after the accumulated standard deviation or a preselected computation time is reached whichever comes rst In the latter case the same geometry is used in a subsequent run until the desired accuracy is obtained The computation time increases both with N and with the desired accuracy and for xed values of these two parameters it increases with the energy of the con guration For these reasons N was chosen by trial and error so as to minimize the computation time for clusters of nuclear geometries with similar energies and varied from 80 000 to 600 000 being mostly about 200 000 The start up trial con guration was the one used previously as were the remaining numerical parameters 25 The density of grid