Large-scale coupled-cluster calculations [Elektronische Ressource] / von Michael Harding

Informations

• Publié par: johannes_gutenberg-universitat_mainz
• Publié le: 01 janvier 2008
• Nombre de lectures: 9
• Langue: English
• Poids de l'ouvrage: 1 Mo

Extrait

Large-Scale Coupled-Cluster Calculations
Dissertation zur Erlangung des Grades
,,Doktor der Naturwissenschaften”
im Promotionsfach Chemie
am Fachbereich Chemie, Pharmazie und Geowissenschaften
der Johannes Gutenberg-Universit¨at in Mainz
von
Michael Harding
geboren in Wiesbaden
Mainz, 20082Contents
1 Introduction 5
2 Mainz-Austin-Budapest version of the ACES II program system 9
3 A computer environment for computational chemistry 11
4 Theoretical foundations 13
4.1 Quantum-chemical methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.1.1 Hartree-Fock theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4.1.2 Møller-Plesset perturbation theory . . . . . . . . . . . . . . . . . . . . 16
4.1.3 Configuration-interaction . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.1.4 Coupled-cluster theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1.5 Density-functional theory . . . . . . . . . . . . . . . . . . . . . . . . . 22
4.2 Analytic derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.1 Hartree-Fock theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.2.2 Coupled-cluster theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.3 Basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.3.1 Correlation-consistent basis sets . . . . . . . . . . . . . . . . . . . . . 28
4.3.2 Basis sets for the calculation of nuclear magnetic shielding constants . 29
4.3.3 Atomic natural orbital basis sets . . . . . . . . . . . . . . . . . . . . . 30
4.3.4 Split-valence basis sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5 Parallel coupled-cluster calculations 31
5.1 Parallelization strategy for coupled-cluster energies and derivatives . . . . . . 31
5.1.1 Parallel algorithm for the perturbative triples contributions
to CCSD(T) energies, gradients, and second derivatives . . . . . . . . 33
5.1.2 Analysis and parallelization of time-determining steps in the CCSD
energy, gradient, and second-derivative calculations . . . . . . . . . . . 36
5.1.3 Further optimization issues . . . . . . . . . . . . . . . . . . . . . . . . 38
5.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6 Computational thermochemistry 45
6.1 High accuracy extrapolated ab initio thermochemistry . . . . . . . . . . . . . 45
6.1.1 Molecular geometries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1.2 HF and CCSD(T) energy . . . . . . . . . . . . . . . . . . . . . . . . . 46
6.1.3 Higher-level correlation effects . . . . . . . . . . . . . . . . . . . . . . 46
3CONTENTS
6.1.4 Zero-point vibrational energies . . . . . . . . . . . . . . . . . . . . . . 47
6.1.5 Diagonal Born-Oppenheimer correction . . . . . . . . . . . . . . . . . 47
6.1.6 Relativistic effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.1.7 Overview and status . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
6.2 Improvements and overview for the HEAT schemes . . . . . . . . . . . . . . . 49
6.2.1 Basis-set convergence of HF-SCF and CCSD(T) . . . . . . . . . . . . 51
6.2.2 Basis-set conv of higher-level correlation effects . . . . . . . . . 53
6.2.3 Core-correlation effects. . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6.2.4 Current best estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.3 High accuracy extrapolated ab initio thermochemistry of vinyl chloride . . . . 65
6.3.1 Differences to the original HEAT protocol . . . . . . . . . . . . . . . . 65
6.3.2 Temperature effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.3.3 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.4 High accuracy extrapolated ab initio thermochemistry of benzene . . . . . . . 70
7 Accurate prediction of nuclear magnetic shielding constants 73
197.1 Quantitative prediction of gas-phase F nuclear magnetic shielding constants 74
7.1.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.1.2 Geometry dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
7.1.3 Electron correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
7.1.4 Basis-set convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7.1.5 Vibrational corrections and temperature effects . . . . . . . . . . . . . 83
7.1.6 Comparison with experimental gas-phase data . . . . . . . . . . . . . 84
7.1.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
137.2 Benchmark calculation for the C NMR chemical shifts of benzene . . . . . . 90
7.3 NMR chemical shifts of the 1-adamantyl cation . . . . . . . . . . . . . . . . . 91
8 Calculation of equilibrium geometries and spectroscopic properties 95
8.1 The geometry of the hydrogen trioxy radical . . . . . . . . . . . . . . . . . . . 97
8.2 The empirical equilibrium structure of diacetylene . . . . . . . . . . . . . . . 100
8.3 Geometry and hyperfinere cyanopolyynes . . . . . . . . . . . . . . . . 106
8.3.1 Geometry and hyperfine structure
of deuterated cyanoacetylene . . . . . . . . . . . . . . . . . . . . . . . 106
8.3.2 Geometry and hyperfine structure cyanobutadiyne and cyanohexatriyne108
8.4 The equilibrium structure of ferrocene . . . . . . . . . . . . . . . . . . . . . . 109
9 Summary 111
Appendix 115
A Technical details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Bibliography 117
41 Introduction
Modern quantum chemistry plays a more and more decisive role in chemical research. Ad-
vances in theoretical methods as well as in computational resources extend the range of
applicability continuously. Nonrelativistic quantum-chemical calculations are based on the
Schr¨odingerequationwhichrepresentsthefundamentalequationforthequantum-mechanical
description of atomic and molecular systems. Due to the fact there is no analytic solution
to this equation for more than two particles, the main objective of quantum chemistry is
to find approximate numerical solutions to this problem. These approximations have to be
classified in terms of accuracy and computational effort. The corresponding applicability of
quantum-chemical methods heavily depends on the required accuracy and the extent of the
molecular system. Small molecules can be described by very accurate but computationally
rather demanding methods, while for extended systems more pragmatic methods need to be
applied.
Coupled-clustertheory[1–3]hasturnedouttobeveryaccurateandreliableattheexpense
ofbeingcomputationallyrathercostly. Withinthisframeworkthecoupled-clustersinglesand
doubles model augmented by a perturbative correction for triple excitations (CCSD(T)) [4]
has become the standard for accurate calculations. This method for example allows the
determination of relative energies within chemical accuracy (ca. 4 kJ/mol). Computational
resources limit the range of applicability for CCSD(T), so that cheaper and less accurate
approximationslikesecond-orderMøller-Plessetperturbationtheory(MP2)[5],Hartree-Fock
(HF) [6], or density-functional theory (DFT) [7,8] have to be used for larger molecular
systems. Extending the range of applicability of highly accurate methods like CCSD(T)
presents one of the challenges in quantum chemistry. Unfortunately the CCSD(T) method
7 1shows a steep operation count scaling ofN , where N is a measure of the system size. This
meansthatdoublingthesizeofthesystemwouldincreasetheoverallexecutiontimebymore
than two orders of magnitude. The advances in computer processor development cannot
combat this steep scaling.
Figure 1.1 shows for the case of Intel processors that the number of transistors in a
state-of-the-art integrated circuit (e.g., a computer processor) is roughly doubling every 24
months [9] for roughly the last four decades. Assuming that the computational performance
2is increasing, at best, linear with the number of transistors leads to the conclusion that we
would expect that it would be 14 years before the dimer of some particular molecule could
be calculated in the same time that is required for the monomer today. In addition to that,
limitations of other computational resources such as size and performance of fast memory,
and disk space have to be taken into account.
1
Assuming that the number of basis functions per atom is fixed.
2
For the sake of simplicity other factors such as clock rate, cache sizes and how many add/multiply oper-
ations could be done within a clock cycle are not discussed.
5Chapter 1: Introduction
2 Xeon 7400
1000000000
Itanium II (9MB cache)
5
Itanium II Core Duo2
100000000
Pentium IV5
Itanium
2
Pentium III10000000
Pentium II5
Pentium
2
804861000000
5
803862
100000 80286
5
80862
10000
5 8080
80082 Number of transistors doubling every 24 month4004
1000
1972 1976 1980 1984 1988 1992 1996 2000 2004 2008
Year
Figure 1.1: Logarithmic plot of the increase in the number of transistors within the last