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ORCA Manual for ab initio, DFT and semiempirical SCF-MO package PDF

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- An ab initio, DFT and semiempirical SCF-MO package -   Version 2.8-20 September 2010 Design  andScientific  Directorship:   Frank Neese Technical  Directorship:   Frank Wennmohs Lehrstuhl  für  Theoretische  Chemie   Wegelerstr.  12D-­‐53115  Bonn,  Germany   [email protected]­‐bonn.de   With  contributions  from:   Ute Becker, Dmitry Ganyushin, Andreas Hansen, Dimitrios G. Liakos, Christian Kollmar, Simone Kossmann, Taras Petrenko, Christoph Reimann, Christoph Riplinger, Kantharuban Sivalingam, Edward Valeev, Boris Wezisla Input  Description TABLE  OF  CONTENTS   1   GENERAL INFORMATION........................................................................................11   1.1   PROGRAM COMPONENTS.............................................................................................11   1.2   UNITS AND CONVERSION FACTORS.............................................................................12   2   PUBLICATIONS RELATED TO ORCA....................................................................13   3   CALLING THE PROGRAM (SERIAL AND PARALLEL).....................................23   3.1   CALLING THE PROGRAM..............................................................................................23   3.2   HINTS ON THE USE OF PARALLEL ORCA.....................................................................26   4   GENERAL STRUCTURE OF THE INPUT FILE.....................................................29   4.1   INPUT BLOCKS............................................................................................................29   4.2   KEYWORD LINES........................................................................................................31   4.3   ORCA AND SYMMETRY.............................................................................................42   4.4   USE OF EFFECTIVE CORE POTENTIALS........................................................................43   4.5   JOBS WITH MULTIPLE STEPS......................................................................................50   5   INPUT OF COORDINATES........................................................................................51   6   RUNNING TYPICAL CALCULATIONS...................................................................54   6.1   SINGLE POINT ENERGIES AND GRADIENTS....................................................................54   6.1.1   Hartree-Fock......................................................................................................54   6.1.1.1   Standard single points.........................................................................................................................54   6.1.1.2   Basis Set Options................................................................................................................................55   6.1.1.3   SCF and Symmetry.............................................................................................................................56   6.1.2   MP2....................................................................................................................59   6.1.2.1   MP2 and RI-MP2 Energies.................................................................................................................59   6.1.2.2   Orbital Optimized MP2 methods........................................................................................................60   6.1.2.3   MP2 and RI-MP2 Gradients...............................................................................................................61   6.1.2.4   Frozen core options............................................................................................................................63   6.1.2.5   MP2 Densities and Natural Orbitals...................................................................................................63   6.1.3   Coupled Cluster and Coupled Pair Methods.....................................................64   6.1.3.1   Basics..................................................................................................................................................64   6.1.3.2   Static versus Dynamic Correlation.....................................................................................................68   6.1.3.3   Basis Sets for Correlated Calculations. The case of ANOs................................................................72   6.1.3.4   Automatic extrapolation to the basis set limit....................................................................................75 Orca Version 2 - Input Description 3   6.1.3.5   Local Coupled Pair and Coupled Cluster Calculations......................................................................79   6.1.4   Density Functional.............................................................................................82   6.1.4.1   Standard Density Functional Calculations.........................................................................................82   6.1.4.2   DFT Calculations with RI...................................................................................................................83   6.1.4.3   Hartree-Fock and Hybrid DFT Calculations with RIJCOSX.............................................................85   6.1.4.4   Hartree-Fock and Hybrid DFT Calculations with RI-JK...................................................................86   6.1.4.5   DFT Calculations with Second Order Perturbative Correction (double hybrid functionals).............87   6.1.4.6   DFT Calculations with Empirical Van der Waals Correction............................................................88   6.1.5   Quadratic Convergence......................................................................................89   6.1.6   Counterpoise Correction....................................................................................91   6.1.7   Complete Active Space Self-Consistent Field.....................................................93   6.1.7.1   Introduction........................................................................................................................................93   6.1.7.2   A simple example...............................................................................................................................94   6.1.7.3   Starting Orbitals..................................................................................................................................96   6.1.7.4   CASSCF and Symmetry...................................................................................................................101   6.1.7.5   RI and RIJCOSX approximations for CASSCF...............................................................................105   6.1.7.6   Breaking Chemical Bonds................................................................................................................106   6.1.7.7   Excited States...................................................................................................................................111   6.1.7.8   CASSCF Natural Orbitals as input for Coupled Cluster Calculations.............................................113   6.1.8   N-Electron Valence State Perturbation Theory (NEVPT2)..............................118   6.1.8.1   Introduction......................................................................................................................................118   6.1.8.2   A simple example.............................................................................................................................119   6.1.8.3   RI Approximation.............................................................................................................................120   6.1.8.4   Parametric surface scans...................................................................................................................120   6.1.8.5   Approximations for large active CASSCF space.............................................................................121   6.1.8.6   State-averaged NEVPT2...................................................................................................................122   6.1.9   Scalar Relativistic SCF.....................................................................................123   6.1.9.1   Douglas-Kroll-Hess..........................................................................................................................123   6.1.9.2   ZORA and IORA..............................................................................................................................124   6.1.10   How to do efficient calculations with atomic natural orbitals?.......................125   6.2   GEOMETRY OPTIMIZATIONS, SURFACE SCANS, TRANSITION STATES, MECPS..........127   6.2.1   Geometry Optimizations..................................................................................127   6.2.2   Numerical Gradients........................................................................................128   6.2.3   Some Notes and Tricks.....................................................................................128   6.2.4   Initial Hessian for minimization.......................................................................129   6.2.5   Coordinate systems for Optimizations..............................................................130   6.2.6   Constrained Optimizations...............................................................................131   6.2.7   Constrained Optimizations for Molecular Clusters (Fragment Optimization).133 Orca Version 2 - Input Description 4   6.2.8   Relaxed Surface Scans......................................................................................135   6.2.9   Multiple XYZ file scans.....................................................................................138   6.2.10   Transition States...............................................................................................138   6.2.10.1   Introduction to Transition State Searches....................................................................................138   6.2.10.2   Hessians for Transition State Calculations..................................................................................141   6.2.10.3   Special Coordinates for Transition State Optimizations..............................................................143   6.2.11   MECP optimization..........................................................................................143   6.2.12   Using the Gaussian optimizer..........................................................................145   6.2.13   ORCA as external optimizer............................................................................146   6.3   VIBRATIONAL FREQUENCIES.....................................................................................146   6.4   REACTION ENERGIES FROM COMPOUND JOBS...........................................................148   6.5   EXCITED STATES WITH CIS, CIS(D) AND TD-DFT..................................................150   6.5.1   General Use......................................................................................................151   6.5.2   Use of TD-DFT for the calculation of X-ray absorption spectra.....................151   6.5.3   Excited state Geometry optimization................................................................155   6.5.4   Doubles correction...........................................................................................155   6.6   MULTIREFERENCE CONFIGURATION INTERACTION AND PERTURBATION THEORY.....156   6.6.1   Introductory Remarks.......................................................................................156   6.6.1.1   Introduction......................................................................................................................................156   6.6.1.2   RI-approximation..............................................................................................................................156   6.6.1.3   Individual Selection..........................................................................................................................157   6.6.1.4   Single excitations..............................................................................................................................157   6.6.1.5   Reference Spaces..............................................................................................................................157   6.6.1.6   Size Consistency...............................................................................................................................158   6.6.1.7   Performance......................................................................................................................................158   6.6.1.8   Symmetry..........................................................................................................................................159   6.6.2   A Tutorial Type Example of a MR Calculation................................................160   6.6.3   Excitation Energies between different multiplicities........................................175   6.6.4   Correlation Energies........................................................................................176   6.6.5   Thresholds........................................................................................................177   6.6.5.1   Reference Values for Total Energies................................................................................................177   6.6.5.2   Convergence of Single Reference Approaches with Respect to T ................................................178   sel 6.6.5.3   Convergence of Multireference Approaches with Respect to T ...................................................178   pre 6.6.6   Energy Differences – Bond Breaking...............................................................180   6.6.7   Energy Differences – Spin Flipping.................................................................182   6.6.8   Potential Energy Surfaces................................................................................184 Orca Version 2 - Input Description 5   6.6.9   Multireference Systems – Ozone.......................................................................187   6.6.10   Size Consistency...............................................................................................189   6.6.11   Efficient MR-MP2 calculations for larger molecules.......................................190   6.7   SOLVATION...............................................................................................................191   6.8   CALCULATION OF PROPERTIES..................................................................................193   6.8.1   Population Analysis and Related Things..........................................................193   6.8.2   Absorption and Fluorescence Bandshapes.......................................................197   6.8.3   IR/Raman spectra, Vibrational Modes and Isotope Shifts...............................202   6.8.3.1   IR Spectra.........................................................................................................................................202   6.8.3.2   Raman Spectra..................................................................................................................................204   6.8.3.3   Resonance Raman Spectra................................................................................................................206   6.8.3.4   NRVS Spectra...................................................................................................................................206   6.8.3.5   Animation of Vibrational Modes......................................................................................................207   6.8.3.6   Isotope Shifts....................................................................................................................................208   6.8.4   Thermochemistry..............................................................................................210   6.8.5   Electric Properties............................................................................................213   6.8.6   NMR Chemical Shifts.......................................................................................214   6.8.7   Hyperfine and Quadrupole Couplings.............................................................216   6.8.8   The EPR g-Tensor and the Zero-Field Splitting Tensor..................................219   6.8.9   ‘Broken-Symmetry’ Wavefunctions and Exchange Couplings.........................221   7   DETAILED DOCUMENTATION.............................................................................224   7.1   MORE ON COORDINATE INPUT..................................................................................224   7.1.1   Fragment Specification....................................................................................224   7.1.2   Defining Geometry Parameters and Scanning Potential Energy Surfaces......225   7.1.3   Inclusion of Point Charges...............................................................................227   7.2   CHOICE OF COMPUTATIONAL MODEL.......................................................................228   7.2.1   Features Common to All Calculations.............................................................228   7.2.2   Density functional calculations........................................................................230   7.2.2.1   Choice of Functional........................................................................................................................230   7.2.2.2   Choice of Integration Grid................................................................................................................235   7.2.2.3   Using the RI-J approximation to the Coulomb part.........................................................................241   7.2.2.4   The Split-RI-J Coulomb Approximation..........................................................................................243   7.2.2.5   Using the RI Approximation for Hartree-Fock and Hybrid DFT (RIJONX)...................................244   7.2.2.6   Using the RI Approximation for Hartree-Fock and Hybrid DFT (RIJCOSX).................................245   7.2.2.7   Improved Analytical Evaluation of the Coulomb term: Split-J........................................................247   7.2.2.8   The Standard Basis Sets and Computational Levels........................................................................247 Orca Version 2 - Input Description 6   7.2.3   Second Order Møller-Plesset Perturbation Theory.........................................248   7.2.4   Semiempirical Methods....................................................................................251   7.3   CHOICE OF BASIS SET...............................................................................................255   7.3.1   Built in Basis Sets.............................................................................................255   7.3.2   Assigning or Adding Basis Functions to an Element.......................................260   7.3.3   Assigning or Adding Basis Functions to Individual Atoms..............................261   7.3.4   Reading orbital and auxiliary basis sets from a file.........................................262   7.4   CHOICE OF INITIAL GUESS AND RESTART OF SCF CALCULATIONS...........................263   7.4.1   AutoStart feature..............................................................................................263   7.4.2   One Electron Matrix Guess..............................................................................264   7.4.3   Basis Set Projection..........................................................................................264   7.4.4   PModel Guess...................................................................................................264   7.4.5   Hueckel and PAtom Guesses............................................................................265   7.4.6   Restarting SCF Calculations............................................................................265   7.4.7   Changing the Order of Initial Guess MOs and Breaking the Initial Guess Symmetry 266   7.5   SCF CONVERGENCE.................................................................................................267   7.5.1   Convergence Tolerances..................................................................................267   7.5.2   Dynamic and Static Damping...........................................................................269   7.5.3   Level Shifting....................................................................................................270   7.5.4   Direct Inversion in Iterative Subspace (DIIS)..................................................270   7.5.5   An alternative DIIS algorithm: KDIIS..............................................................271   7.5.6   Approximate Second Order SCF (SOSCF)......................................................271   7.5.7   Full Second Order SCF (NR)...........................................................................272   7.5.8   Fractional Occupation Numbers......................................................................275   7.6   CHOICE OF WAVEFUNCTION AND INTEGRAL HANDLING...........................................276   7.6.1   Choice of Wavefunction Type...........................................................................276   7.6.2   UHF Natural Orbitals......................................................................................279   7.6.3   Integral Handling (Conventional, Direct, SemiDirect)....................................279   7.7   THE SECOND ORDER MANY BODY PERTURBATION THEORY MODULE (MP2)..........283   7.7.1   Standard MP2...................................................................................................283   7.7.2   RI-MP2.............................................................................................................284   7.7.3   Orbital Optimized MP2....................................................................................292 Orca Version 2 - Input Description 7   7.7.4   RICOSX-RI-MP2 Gradients.............................................................................296   7.8   THE SINGLE REFERENCE CORRELATION MODULE....................................................297   7.8.1   Theory...............................................................................................................297   7.8.2   Closed shell equations......................................................................................301   7.8.3   Open shell equations (spin-unrestricted formalism)........................................305   7.8.4   Use of the MDCI Module.................................................................................305   7.9   THE COMPLETE ACTIVE SPACE SELF-CONSISTENT FIELD (CASSCF) MODULE........307   7.9.1   General Description.........................................................................................307   7.9.2   CASSCF Properties.........................................................................................318   7.10   N-ELECTRON VALENCE STATE PERTURBATION THEORY......................................319   7.11   RELATIVISTIC OPTIONS.........................................................................................320   7.12   GEOMETRY OPTIMIZATION....................................................................................324   7.13   EXCITED STATES VIA CIS AND TD-DFT................................................................342   7.13.1   General Features..............................................................................................343   7.13.2   Semiempirical Methods....................................................................................344   7.13.3   HF-Wavefunctions............................................................................................347   7.13.4   Non-Hybrid DFT..............................................................................................347   7.13.5   Hybrid DFT......................................................................................................349   7.13.6   Doubles Correction..........................................................................................349   7.13.7   Computational Aspects.....................................................................................351   7.13.7.1   RI approximation (AO-basis).......................................................................................................351   7.13.7.2   RI approximation (MO-basis)......................................................................................................351   7.13.7.3   Integral Handling.........................................................................................................................352   7.13.7.4   Valence versus Rydberg states.....................................................................................................352   7.13.7.5   Asymptotatically Corrected Density Functionals........................................................................353   7.13.7.6   Potential Energy Surface Scans...................................................................................................356   7.13.7.7   Potential Energy Surface Scans along Normal Coordinates........................................................357   7.13.7.8   Normal Mode Scan Calculations Between Different Structures..................................................361   7.14   THE MULTIREFERENCE CORRELATION MODULE...................................................363   7.14.1   General Description of the Correlation Module..............................................363   7.14.2   The SOC Submodule of the MRCI Module....................................................367   7.14.2.1   Calculation of the Spin-Spin Coupling and Spin-Orbit Coupling and Effects............................367   7.14.2.2   Magnetic fields in MRCI.............................................................................................................375   7.14.2.3   g-tensor calculations.....................................................................................................................376   7.14.2.4   Relativistic Picture Change in Douglas Kroll SOC and Zeeman operators.................................377   7.14.2.5   MCD and Absorption Spectra Calculation and Generation.........................................................378 Orca Version 2 - Input Description 8   7.15   SIMULATION AND FIT OF VIBRONIC STRUCTURE IN ELECTRONIC SPECTRA, RESONANCE RAMAN EXCITATION PROFILES AND SPECTRA WITH THE ORCA_ASA PROGRAM...................382   7.15.1   General Description of the Program................................................................383   7.15.2   Spectral Simualtion Procedures: Input Structure and Model Parameters.......384   7.15.2.1   Example: Simple Model...............................................................................................................384   7.15.2.2   Example: Modelling of Absorption and Fluorescence Spectra within the IMDHO Model........386   7.15.2.3   Example: Modelling of Absorption and Fluorescence Spectra within the IMDHOFA Model...389   7.15.2.4   Example: Modelling of Effective Broadening, Effective Stokes Shift and Temperature Effects in Absorption and Fluorescence Spectra within the IMDHO Model.....................................................................390   7.15.2.5   Example: Modelling of Absorption and Resonance Raman Spectra for the 1-1A →1-1B Transition in 1,3,5 g u trans-hexatriene..................................................................................................................................................393   7.15.2.6   Example: Modelling of Absorption spectrum and Resonance Raman Profiles for the 1-1A →1-1B g u Transition in 1,3,5 trans-hexatriene...................................................................................................................397   7.15.3   Fitting of Experimental Spectra.......................................................................399   7.15.3.1   Example: Gauss-Fit of Absorption Spectrum..............................................................................399   7.15.3.2   Example: Fit of Absorption and Resonance Raman Spectra for 1-1A →1-1B transition in 1,3,5 trans- g u hexatriene 406   7.15.3.3   Example: Single-Mode Fit of Absorption and Fluorescence Spectra for 1-1A →1-1B transition in g 2u Tetracene 413   7.15.4   Quantum-Chemically Assisted Simulations and Fits of Optical Bandshapes and Resonance Raman Intensities.........................................................................................417   7.15.4.1   Example: Quantum-Chemically Assisted Analysis and Fit of the Absorption and Resonance Raman Spectra for the 1-1A →1-1B Transition in 1,3,5 trans-hexatriene.................................................................................418   g u 7.15.4.2   Important Notes about Proper Comparison of Experimental and Quantum Chemically Calculated Resonance Raman Spectra.................................................................................................................................426   7.15.4.3   Example: Normal mode scan calculations of model paramters for 1-1A →1-1B transition in 1,3,5 trans- g u hexatriene 428   7.16   THE COSMO SOLVATION MODEL........................................................................430   7.17   CALCULATION OF PROPERTIES..............................................................................433   7.17.1   Electric Properties............................................................................................433   7.17.2   The Spin-Orbit Coupling Operator..................................................................433   7.17.3   The EPR/NMR Module.....................................................................................436   7.17.3.1   Hyperfine and Quadrupole Couplings.........................................................................................437   7.17.3.2   The g-tensor.................................................................................................................................440   7.17.3.3   Zero-Field-Splitting......................................................................................................................441   GENERAL TREATMENT........................................................................................................443   7.18   POPULATIONS ANALYSIS AND CONTROL OF OUTPUT.............................................450   7.18.1   Controlling Output...........................................................................................450 Orca Version 2 - Input Description 9   7.18.2   Mulliken Population Analysis...........................................................................452   7.18.3   Löwdin Population Analysis.............................................................................453   7.18.4   Mayer Population Analysis..............................................................................454   7.18.5   Natural Population Analysis............................................................................455   7.18.6   UNO Orbital Printing.......................................................................................460   7.19   ORBITAL AND DENSITY PLOTS...............................................................................460   7.19.1   Contour Plots....................................................................................................460   7.19.2   Surface Plots.....................................................................................................462   7.19.2.1   General Points..............................................................................................................................462   7.19.2.2   Interface to gOpenMol.................................................................................................................464   7.19.2.3   Interface to Molekel.....................................................................................................................465   7.20   UTILITY PROGRAMS...............................................................................................466   7.20.1   orca_mapspc.....................................................................................................466   7.20.2   orca_chelpg......................................................................................................467   7.20.3   orca_pltvib........................................................................................................467   7.20.4   orca_vib............................................................................................................468   7.20.5   orca_plot...........................................................................................................468   7.20.6   orca_2mkl: Old Molekel as well as MolDen inputs.........................................468   7.20.7   orca_vpot..........................................................................................................469   8   SOME TIPS AND TRICKS (UPDATED DECEMBER 2009)................................469   8.1   COST VERSUS ACCURACY.........................................................................................469   8.2   CONVERGING SCF CALCULATIONS...........................................................................473   8.3   CHOICE OF THEORETICAL METHOD..........................................................................474   9   LITERATURE..............................................................................................................477   SUMMARY OF REVISIONS............................................................................................480 Orca Version 2 - Input Description 10 Foreword   The  ORCA  project  is  now  almost  10  years  old  and  it  is  probably  fair  to  say  that  the  program  has  significantly  matured  over  the  past  years.   It  is  now  used  by  almost  4000  individuals  or  research  groups  and  is  installed  at  dozens  if  not  hundreds  of  supercomputer  centers   worldwide.  We  feel  strongly  encouraged  by  this  fact  and  it  is  our  pleasure  to  further  develop  the  program  for  the  benefit  of  the   computational  chemistry  and  spectroscopy  communities.     Since  2006  when  the  group  moved  to  the  university  of  Bonn,  there  has  been  a  gradual  shift  in  the  focus  of  the  development  from  special   spectroscopy  to  more  general  purpose  quantum  chemistry.  This  was  made  possible  because  the  development  group  has  considerably   grown  and  highly  talented  and  motivated  students  continued  to  bring  in  new  features  in  and  greatly  improved  existing  ones.  The  areas  that   are  perhaps  most  active  in  future  developments  concern  simplified  wavefunction  methods  or  the  single  reference  type  (MP2  and  local   coupled  pair/coupled  cluster  methods)  and  new  density  functionals  (in  particular  double  hybrid  functional).  An  area  that  will  see  more   activity  in  the  future  is  multireference  theory.       However,  with  all  developments  in  improved  wavefunctions,  a  focus  of  the  program  will  remain  theoretical  spectroscopy  and  we  plan  to   further  enhance    the  programs  capabilities  in  this  area.     Finally,  performance,  parallelization  robustness  and  user  friendliness  are  subjects  that  are  high  on  our  priority  list.     As  always,  we  appreciate  positive  as  well  as  negative  feedback  from  our  growing  group  of  users  and  hope  that  you  enjoy  using  the  program   as  much  as  we  enjoy  developing  it.  As  ORCA  is  strictly  non-­‐commercial  you  can  count  on  the  fact  that  it  will  remain  free  of  charge.  The   best  way  to  show  your  appreciation  of  our  efforts  is  to  cite  our  original  research  and  development  papers  in  your  own  work.  This  will   provide  us  with  the  possibility  of  raising  sufficient  funding  for  continuing  to  do  what  we  enjoy  most  –  develop  quantum  chemistry!       Frank  Neese,  December  2009

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University of Bonn, 2010. — 489 p. Version 2.8-20 September 2010Manual for Quantum Chemistry computational package ORCA. ORCA package is free of charge and can be installed on all computation facilities.This manual provides a description and explanation on how to set up Ab initio, HF, DFT, TD-DFT,
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