Modern Quantum Chemistry with [Open]Molcas
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Correlation.Pdf
INTRODUCTION TO THE ELECTRONIC CORRELATION PROBLEM PAUL E.S. WORMER Institute of Theoretical Chemistry, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands Contents 1 Introduction 2 2 Rayleigh-SchrÄodinger perturbation theory 4 3 M¿ller-Plesset perturbation theory 7 4 Diagrammatic perturbation theory 9 5 Unlinked clusters 14 6 Convergence of MP perturbation theory 17 7 Second quantization 18 8 Coupled cluster Ansatz 21 9 Coupled cluster equations 26 9.1 Exact CC equations . 26 9.2 The CCD equations . 30 9.3 CC theory versus MP theory . 32 9.4 CCSD(T) . 33 A Hartree-Fock, Slater-Condon, Brillouin 34 B Exponential structure of the wavefunction 37 C Bibliography 40 1 1 Introduction These are notes for a six hour lecture series on the electronic correlation problem, given by the author at a Dutch national winterschool in 1999. The main purpose of this course was to give some theoretical background on the M¿ller-Plesset and coupled cluster methods. Both computational methods are available in many quantum chemical \black box" programs. The audi- ence consisted of graduate students, mostly with an undergraduate chemistry education and doing research in theoretical chemistry. A basic knowledge of quantum mechanics and quantum chemistry is pre- supposed. In particular a knowledge of Slater determinants, Slater-Condon rules and Hartree-Fock theory is a prerequisite of understanding the following notes. In Appendix A this theory is reviewed briefly. Because of time limitations hardly any proofs are given, the theory is sketchily outlined. No attempt is made to integrate out the spin, the theory is formulated in terms of spin-orbitals only. -
Effective Hamiltonians Derived from Equation-Of-Motion Coupled-Cluster
Effective Hamiltonians derived from equation-of-motion coupled-cluster wave-functions: Theory and application to the Hubbard and Heisenberg Hamiltonians Pavel Pokhilkoa and Anna I. Krylova a Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 Effective Hamiltonians, which are commonly used for fitting experimental observ- ables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not triv- ial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled- cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed. I. INTRODUCTION Coarse graining is commonly used in computational chemistry and physics. It is ex- ploited in a number of classic models serving as a foundation of modern solid-state physics: tight binding[1, 2], Drude{Sommerfeld's model[3{5], Hubbard's [6] and Heisenberg's[7{9] Hamiltonians. These models explain macroscopic properties of materials through effective interactions whose strengths are treated as model parameters. The values of these pa- rameters are determined either from more sophisticated theoretical models or by fitting to experimental observables. -
Electronic Supporting Information a New Class of Soluble and Stable Transition-Metal-Substituted Polyoxoniobates: [Cr2(OH)4Nb10o
Electronic Supplementary Material (ESI) for Dalton Transactions This journal is © The Royal Society of Chemistry 2012 Electronic Supporting Information A New Class of Soluble and Stable Transition-Metal-Substituted Polyoxoniobates: [Cr2(OH)4Nb10O30]8-. Jung-Ho Son, C. André Ohlin and William H. Casey* A) Computational Results The two most interesting aspects of this new polyoxoanion is the inclusion of a more redox active metal and the optical activity in the visible region. For these reasons we in particular wanted to explore whether it was possible to readily and routinely predict the location of the absorbance bands of this type of compound. Also, owing to the difficulty in isolating the oxidised and reduced forms of the central polyanion dichromate species, we employed computations at the density functional theory (DFT) level to get a better idea of the potential characteristics of these forms. Structures were optimised for anti-parallel and parallel electronic spin alignments, and for both high and low spin cases where relevant. Intermediate spin configurations were 8- II III also tested for [Cr2(OH)4Nb10O30] . As expected, the high spin form of the Cr Cr complex was favoured (Table S1, below). DFT overestimates the bond lengths in general, but gives a good picture of the general distortion of the octahedral chromium unit, and in agreement with the crystal structure predicts that the shortest bond is the Cr-µ2-O bond trans from the central µ6- oxygen in the Lindqvist unit, and that the (Nb-)µ2-O-Cr-µ4-O(-Nb,Nb,Cr) angle is smaller by ca 5˚ from the ideal 180˚. -
Computer-Assisted Catalyst Development Via Automated Modelling of Conformationally Complex Molecules
www.nature.com/scientificreports OPEN Computer‑assisted catalyst development via automated modelling of conformationally complex molecules: application to diphosphinoamine ligands Sibo Lin1*, Jenna C. Fromer2, Yagnaseni Ghosh1, Brian Hanna1, Mohamed Elanany3 & Wei Xu4 Simulation of conformationally complicated molecules requires multiple levels of theory to obtain accurate thermodynamics, requiring signifcant researcher time to implement. We automate this workfow using all open‑source code (XTBDFT) and apply it toward a practical challenge: diphosphinoamine (PNP) ligands used for ethylene tetramerization catalysis may isomerize (with deleterious efects) to iminobisphosphines (PPNs), and a computational method to evaluate PNP ligand candidates would save signifcant experimental efort. We use XTBDFT to calculate the thermodynamic stability of a wide range of conformationally complex PNP ligands against isomeriation to PPN (ΔGPPN), and establish a strong correlation between ΔGPPN and catalyst performance. Finally, we apply our method to screen novel PNP candidates, saving signifcant time by ruling out candidates with non‑trivial synthetic routes and poor expected catalytic performance. Quantum mechanical methods with high energy accuracy, such as density functional theory (DFT), can opti- mize molecular input structures to a nearby local minimum, but calculating accurate reaction thermodynamics requires fnding global minimum energy structures1,2. For simple molecules, expert intuition can identify a few minima to focus study on, but an alternative approach must be considered for more complex molecules or to eventually fulfl the dream of autonomous catalyst design 3,4: the potential energy surface must be frst surveyed with a computationally efcient method; then minima from this survey must be refned using slower, more accurate methods; fnally, for molecules possessing low-frequency vibrational modes, those modes need to be treated appropriately to obtain accurate thermodynamic energies 5–7. -
Dalton2018.0 – Lsdalton Program Manual
Dalton2018.0 – lsDalton Program Manual V. Bakken, A. Barnes, R. Bast, P. Baudin, S. Coriani, R. Di Remigio, K. Dundas, P. Ettenhuber, J. J. Eriksen, L. Frediani, D. Friese, B. Gao, T. Helgaker, S. Høst, I.-M. Høyvik, R. Izsák, B. Jansík, F. Jensen, P. Jørgensen, J. Kauczor, T. Kjærgaard, A. Krapp, K. Kristensen, C. Kumar, P. Merlot, C. Nygaard, J. Olsen, E. Rebolini, S. Reine, M. Ringholm, K. Ruud, V. Rybkin, P. Sałek, A. Teale, E. Tellgren, A. Thorvaldsen, L. Thøgersen, M. Watson, L. Wirz, and M. Ziolkowski Contents Preface iv I lsDalton Installation Guide 1 1 Installation of lsDalton 2 1.1 Installation instructions ............................. 2 1.2 Hardware/software supported .......................... 2 1.3 Source files .................................... 2 1.4 Installing the program using the Makefile ................... 3 1.5 The Makefile.config ................................ 5 1.5.1 Intel compiler ............................... 5 1.5.2 Gfortran/gcc compiler .......................... 9 1.5.3 Using 64-bit integers ........................... 12 1.5.4 Using Compressed-Sparse Row matrices ................ 13 II lsDalton User’s Guide 14 2 Getting started with lsDalton 15 2.1 The Molecule input file ............................ 16 2.1.1 BASIS ................................... 17 2.1.2 ATOMBASIS ............................... 18 2.1.3 User defined basis sets .......................... 19 2.2 The LSDALTON.INP file ............................ 21 3 Interfacing to lsDalton 24 3.1 The Grand Canonical Basis ........................... 24 3.2 Basisset and Ordering .............................. 24 3.3 Normalization ................................... 25 i CONTENTS ii 3.4 Matrix File Format ................................ 26 3.5 The lsDalton library bundle .......................... 27 III lsDalton Reference Manual 29 4 List of lsDalton keywords 30 4.1 **GENERAL ................................... 31 4.1.1 *TENSOR ............................... -
Quantum Chemistry on a Grid
Quantum Chemistry on a Grid Lucas Visscher Vrije Universiteit Amsterdam 1 Outline Why Quantum Chemistry needs to be gridified Computational Demands Other requirements What may be expected ? Program descriptions Dirac • Organization • Distributed development and testing Dalton Amsterdam Density Functional (ADF) An ADF-Dalton-Dirac grid driver Design criteria Current status Quantum Chemistry on the Grid, 08-11-2005 L. Visscher, Vrije Universiteit Amsterdam 2 Computational (Quantum) Chemistry QC is traditionally run on supercomputers Large fraction of the total supercomputer time annually allocated Characteristics Compute Time scales cubically or higher with number of atoms treated. Typical : a few hours to several days on a supercomputer Memory Usage scales quadratically or higher with number of atoms. Typical : A few hundred MB till tens of GB Data Storage variable. Typical: tens of Mb till hundreds of GB. Communication • Often serial (one-processor) runs in production work • Parallelization needs sufficient band width. Typical lower limit 100 Mb/s. Quantum Chemistry on the Grid, 08-11-2005 L. Visscher, Vrije Universiteit Amsterdam 3 Changing paradigms in quantum chemistry Computable molecules are often already “large” enough Many degrees of freedom Search for global minimum energy is less important Statistical sampling of different conformations is desired Let the nuclei move, follow molecules that evolve in time 2 steps : (Quantum) dynamics on PES 1 step : Classical dynamics with forces computed via QM Changing characteristics General: more similar calculations Compute time : Increases : more calculations Memory usage : Stays constant : typical size remains the same Data storage : Decreases : intermediate results are less important Communication: Decreases : only start-up data and final result Quantum Chemistry on the Grid, 08-11-2005 L. -
Computational Studies of the Unusual Water Adduct [Cp2time (OH2)]: the Roles of the Solvent and the Counterion
Dalton Transactions View Article Online PAPER View Journal | View Issue Computational studies of the unusual water + adduct [Cp2TiMe(OH2)] : the roles of the Cite this: Dalton Trans., 2014, 43, 11195 solvent and the counterion† Jörg Saßmannshausen + The recently reported cationic titanocene complex [Cp2TiMe(OH2)] was subjected to detailed computational studies using density functional theory (DFT). The calculated NMR spectra revealed the importance of including the anion and the solvent (CD2Cl2) in order to calculate spectra which were in good agreement Received 29th January 2014, with the experimental data. Specifically, two organic solvent molecules were required to coordinate to Accepted 19th March 2014 the two hydrogens of the bound OH2 in order to achieve such agreement. Further elaboration of the role DOI: 10.1039/c4dt00310a of the solvent led to Bader’s QTAIM and natural bond order calculations. The zirconocene complex + www.rsc.org/dalton [Cp2ZrMe(OH2)] was simulated for comparison. Creative Commons Attribution-NonCommercial 3.0 Unported Licence. Introduction Group 4 metallocenes have been the workhorse for a number of reactions for some decades now. In particular the cationic + compounds [Cp2MR] (M = Ti, Zr, Hf; R = Me, CH2Ph) are believed to be the active catalysts for a number of polymeriz- – ation reactions such as Kaminsky type α-olefin,1 10 11–15 16–18 This article is licensed under a carbocationic or ring-opening lactide polymerization. For these highly electrophilic cationic compounds, water is usually considered a poison as it leads to catalyst decompo- sition. In this respect it was quite surprising that Baird Open Access Article. Published on 21 March 2014. -
Møller–Plesset Perturbation Theory: from Small Molecule Methods to Methods for Thousands of Atoms Dieter Cremer∗
Advanced Review Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms Dieter Cremer∗ The development of Møller–Plesset perturbation theory (MPPT) has seen four dif- ferent periods in almost 80 years. In the first 40 years (period 1), MPPT was largely ignored because the focus of quantum chemists was on variational methods. Af- ter the development of many-body perturbation theory by theoretical physicists in the 1950s and 1960s, a second 20-year long period started, during which MPn methods up to order n = 6 were developed and computer-programed. In the late 1980s and in the 1990s (period 3), shortcomings of MPPT became obvious, espe- cially the sometimes erratic or even divergent behavior of the MPn series. The physical usefulness of MPPT was questioned and it was suggested to abandon the theory. Since the 1990s (period 4), the focus of method development work has been almost exclusively on MP2. A wealth of techniques and approaches has been put forward to convert MP2 from a O(M5) computational problem into a low- order or linear-scaling task that can handle molecules with thousands of atoms. In addition, the accuracy of MP2 has been systematically improved by introducing spin scaling, dispersion corrections, orbital optimization, or explicit correlation. The coming years will see a continuously strong development in MPPT that will have an essential impact on other quantum chemical methods. C 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 509–530 DOI: 10.1002/wcms.58 INTRODUCTION Hylleraas2 on the description of two-electron prob- erturbation theory has been used since the early lems with the help of perturbation theory. -
Coupled Cluster Methods in Quantum Chemistry
Title: Coupled Cluster methods in quantum chemistry Name: Thorsten Rohwedder, Reinhold Schneider Al./Addr.: Technische UniversitatBerlin Coupled Cluster methods in quantum chemistry Short description Coupled Cluster methods applied in quantum chemistry reformulate the electronic Schrodinger equation as a nonlinear equation, enabling the computation of size- consistent high-precision approximations of the ground state solution for weakly cor- related systems. Introduction The Coupled Cluster method (CC method) is one of the most successful and frequently used approaches for the computation of atomic and molecular electronic structure, i.e. for the solution of the stationary electronic Schrodinger equation, whenever high ac- curacy is required. In contrast to Hartree-Fock type methods (HF) or methods from density functional theory (see the respective entries in this work), high accuracy meth- ods have to account in particular for the quantum-mechanical phenomenon of electronic correlation. If a preliminarily calculated reference solution { usually provided by a HF calculation { already is a good approximation to the sought ground state wave func- tion, the problem is said to be weakly correlated. CC as a post-Hartree-Fock method (also see the entry by M. Lewin) then enables an ecient, accurate and size-extensive description of solutions of the electronic Schrodingerequation. In this context, the 2 size-extensivity of the CC approach is a key aspect, re ecting the correct scaling of correlation energy with respect to the number of electrons. CC methods were initially developed for the treatment of many body quantum systems in nuclear physics in the 1950s and were used for quantum chemical calculations since the 1966 initial work by Paldus and Czek,see (Czek,1991) for a historical overview. -
1 Installation Guide for Columbus Version 7.1 with Openmolcas Support (Colmol-2.1.0)
1 Installation Guide for Columbus Version 7.1 with OpenMolcas Support (colmol-2.1.0) 1.1 Overview Columbus and Molcas cooperate by exchanging well-defined, transferable quantities, specif- ically AO integrals, AO density matrices and MO coefficients in the native Molcas format by using library functions from the Molcas library. Additionally, the RunFile is processed, which is used by Molcas to store additional information often required to be passed in between dif- ferent Molcas modules. Molcas provides some mechanism to incorporate external programs and making them accessible through the standard Molcas input file. Since it is necessary to link a portion of the Molcas library, both Columbus and Molcas must be compiled and linked in a compatible way, that is to say (i) the same compilers and (ii) compatible compiler options. Hence, both codes cooperate on a binary level and do not rely on some file conversion utilities. Please note, that the Molcas library is frequently restructured, so that files produced with a previous version may or may not be compatible with the current version of Molcas (cf. page 4). Additionally, there are now two molcas driver utilities: molcas.exe in Molcas-8.2 developer version and pymolcas in the OpenMolcas version, which may not behave exactly the same way. 1.2 New Features Primarily, rewritten versions of the SCF, MCSCF, AO-MO transformation and CI-gradient code are introduced. With exception of the CI gradient code, all codes are now parallel and make extensive use of shared memory and much more efficient intermediate data storage. The same driver (columbus.exe) now also supports an old modified version of the dalton code (affecting primarily the integral and density matrix handling and storage format in the old HERMIT and ABACUS code portions). -
A Summary of ERCAP Survey of the Users of Top Chemistry Codes
A survey of codes and algorithms used in NERSC chemical science allocations Lin-Wang Wang NERSC System Architecture Team Lawrence Berkeley National Laboratory We have analyzed the codes and their usages in the NERSC allocations in chemical science category. This is done mainly based on the ERCAP NERSC allocation data. While the MPP hours are based on actually ERCAP award for each account, the time spent on each code within an account is estimated based on the user’s estimated partition (if the user provided such estimation), or based on an equal partition among the codes within an account (if the user did not provide the partition estimation). Everything is based on 2007 allocation, before the computer time of Franklin machine is allocated. Besides the ERCAP data analysis, we have also conducted a direct user survey via email for a few most heavily used codes. We have received responses from 10 users. The user survey not only provide us with the code usage for MPP hours, more importantly, it provides us with information on how the users use their codes, e.g., on which machine, on how many processors, and how long are their simulations? We have the following observations based on our analysis. (1) There are 48 accounts under chemistry category. This is only second to the material science category. The total MPP allocation for these 48 accounts is 7.7 million hours. This is about 12% of the 66.7 MPP hours annually available for the whole NERSC facility (not accounting Franklin). The allocation is very tight. The majority of the accounts are only awarded less than half of what they requested for. -
Trends in Atomistic Simulation Software Usage [1.3]
A LiveCoMS Perpetual Review Trends in atomistic simulation software usage [1.3] Leopold Talirz1,2,3*, Luca M. Ghiringhelli4, Berend Smit1,3 1Laboratory of Molecular Simulation (LSMO), Institut des Sciences et Ingenierie Chimiques, Valais, École Polytechnique Fédérale de Lausanne, CH-1951 Sion, Switzerland; 2Theory and Simulation of Materials (THEOS), Faculté des Sciences et Techniques de l’Ingénieur, École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; 3National Centre for Computational Design and Discovery of Novel Materials (MARVEL), École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland; 4The NOMAD Laboratory at the Fritz Haber Institute of the Max Planck Society and Humboldt University, Berlin, Germany This LiveCoMS document is Abstract Driven by the unprecedented computational power available to scientific research, the maintained online on GitHub at https: use of computers in solid-state physics, chemistry and materials science has been on a continuous //github.com/ltalirz/ rise. This review focuses on the software used for the simulation of matter at the atomic scale. We livecoms-atomistic-software; provide a comprehensive overview of major codes in the field, and analyze how citations to these to provide feedback, suggestions, or help codes in the academic literature have evolved since 2010. An interactive version of the underlying improve it, please visit the data set is available at https://atomistic.software. GitHub repository and participate via the issue tracker. This version dated August *For correspondence: 30, 2021 [email protected] (LT) 1 Introduction Gaussian [2], were already released in the 1970s, followed Scientists today have unprecedented access to computa- by force-field codes, such as GROMOS [3], and periodic tional power.