5. Spectroscopy and Properties

Spectroscopy and Properties

• 5.1. Population Analysis
  • 5.1.1. Mulliken Population Analysis
    • 5.1.1.1. Basic Usage
  • 5.1.2. Löwdin Population Analysis
    • 5.1.2.1. Basic Usage
  • 5.1.3. Frontier Molecular Orbital Populations
  • 5.1.4. Mayer Population Analysis
    • 5.1.4.1. Basic Usage
  • 5.1.5. Natural Population Analysis
    • 5.1.5.1. Basic Usage
  • 5.1.6. Hirshfeld Population Analysis
    • 5.1.6.1. Basic Usage
    • 5.1.6.2. Example
  • 5.1.7. MBIS Charges
    • 5.1.7.1. Basic Usage
    • 5.1.7.2. MBIS Quantities
    • 5.1.7.3. Example
  • 5.1.8. CHELPG Charges
    • 5.1.8.1. Basic Usage
  • 5.1.9. RESP Charges
  • 5.1.10. Local Spin Analysis
  • 5.1.11. Population Analysis of UNOs
  • 5.1.12. Keywords
• 5.2. Natural Bond Orbital (NBO) Analysis
  • 5.2.1. NBO Deletions
  • 5.2.2. NBO for Post-HF Densities
  • 5.2.3. Natural Chemical Shielding Analysis (NCS)
• 5.3. Fractional Occupation Number Weighted Density (FOD)
  • 5.3.1. Basic Usage
  • 5.3.2. FOD Plots
  • 5.3.3. Example: p-Benzyne
• 5.4. Excited States Calculations
  • 5.4.1. Excited States with RPA, CIS, TD-DFT and SF-TDA
    • 5.4.1.1. General Use
    • 5.4.1.2. Capabilities
  • 5.4.2. Excited States with Restricted Open-shell CIS - ROCIS
    • 5.4.2.1. General Use
    • 5.4.2.2. Capabilities
  • 5.4.3. Excited States for Open-Shell Molecules with CASSCF Linear Response (MC-RPA)
    • 5.4.3.1. General Use
    • 5.4.3.2. Capabilities
  • 5.4.4. Excited States with ADC2
    • 5.4.4.1. General Use
    • 5.4.4.2. Capabilities
  • 5.4.5. Excited States with STEOM-CCSD
    • 5.4.5.1. General Use
    • 5.4.5.2. Capabilities
  • 5.4.6. Excited States with IH-FSMR-CCSD
    • 5.4.6.1. General Use
    • 5.4.6.2. Capabilities
  • 5.4.7. Excited States with PNO based coupled cluster methods
    • 5.4.7.1. General Use
    • 5.4.7.2. Capabilities
  • 5.4.8. Excited States with DLPNO based coupled cluster methods
    • 5.4.8.1. General Use
• 5.5. Excited State Dynamics
  • 5.5.1. Absorption Spectrum
    • 5.5.1.1. The ideal model, Adiabatic Hessian (AH)
    • 5.5.1.2. The simplest model, Vertical Gradient (VG)
    • 5.5.1.3. A better model, Adiabatic Hessian After a Step (AHAS)
    • 5.5.1.4. Other PES options
    • 5.5.1.5. Duschinsky rotations
    • 5.5.1.6. Temperature effects
    • 5.5.1.7. Multistate Spectrum
  • 5.5.2. Fluorescence Rates and Spectrum
    • 5.5.2.1. General Aspects
    • 5.5.2.2. Rates and Examples
  • 5.5.3. Phosphorescence Rates and Spectrum
    • 5.5.3.1. General Aspects
    • 5.5.3.2. Calculation of rates
  • 5.5.4. Intersystem Crossing Rates (unpublished)
    • 5.5.4.1. General Aspects
    • 5.5.4.2. ISC, TD-DFT and the HT effect
  • 5.5.5. Internal Conversion Rates (unpublished)
  • 5.5.6. Resonant Raman Spectrum
    • 5.5.6.1. General Aspects
    • 5.5.6.2. Isotopic Labeling
    • 5.5.6.3. RRaman and Linewidths
  • 5.5.7. ESD and STEOM-CCSD or other higher level methods - the APPROXADEN option
  • 5.5.8. Circularly Polarized Spectroscopies
    • 5.5.8.1. General Aspects of the Theory
    • 5.5.8.2. Vibration effects on ECD spectra
    • 5.5.8.3. Computation of CP-FLUOR vs CP-PHOS spectra. The case of \(C_{3}H_{6}O\).
    • 5.5.8.4. Use of ABS, ECD PL and CPL as a routine analysis computational tools
  • 5.5.9. Magnetic Circular Dichroism
    • 5.5.9.1. General Aspects of the Theory
    • 5.5.9.2. Specific Keywords and recommendations
  • 5.5.10. Tips, Tricks and Troubleshooting
  • 5.5.11. More on the Excited State Dynamics module
    • 5.5.11.1. Absorption and Emission Rates and Spectrum
      • 5.5.11.1.1. General Aspects of the Theory
      • 5.5.11.1.2. Approximations to the excited state PES
      • 5.5.11.1.3. Mixing methods
      • 5.5.11.1.4. Removal of frequencies
    • 5.5.11.2. Normal modes coordinate systems
      • 5.5.11.2.1. Geometry rotation and Duschinsky matrices
      • 5.5.11.2.2. Derivatives of the transition dipole
      • 5.5.11.2.3. The Fourier Transform step
      • 5.5.11.2.4. Spectrum options
      • 5.5.11.2.5. General
    • 5.5.11.3. Intersystem crossing rates
      • 5.5.11.3.1. General Aspects of the Theory
      • 5.5.11.3.2. Tips and Tricks
    • 5.5.11.4. Resonant Raman Spectrum
      • 5.5.11.4.1. General Aspects of the Theory
      • 5.5.11.4.2. Specific Keywords and Details
  • 5.5.12. Complete Keyword List for the ESD Module
• 5.6. Excited States via RPA, CIS, TD-DFT and SF-TDA
  • 5.6.1. General Features
  • 5.6.2. Semiempirical Methods
  • 5.6.3. Hartree-Fock Wavefunctions
  • 5.6.4. Non-Hybrid and Hybrid DFT
  • 5.6.5. Collinear Spin-Flip TDA (SF-TD-DFT)
    • 5.6.5.1. First example: methylene and SF-CIS
    • 5.6.5.2. Benzyne and SF-TDA
  • 5.6.6. Including solvation effects via LR-CPCM theory
    • 5.6.6.1. Equilibrium and non-equilibrium conditions
  • 5.6.7. Population Analysis of Excited States
  • 5.6.8. Simplified TDA and TD-DFT
    • 5.6.8.1. Theoretical Background
    • 5.6.8.2. Calculation Set-up
  • 5.6.9. Double-hybrid functionals and Doubles Correction
  • 5.6.10. Spin-orbit coupling
    • 5.6.10.1. SOC and ECPs
  • 5.6.11. Natural Transition Orbitals
  • 5.6.12. Computational Aspects
    • 5.6.12.1. RI Approximation (AO-Basis)
    • 5.6.12.2. Integral Handling
    • 5.6.12.3. Valence versus Rydberg States
    • 5.6.12.4. Restrictions for Range-Separated Density Functionals
    • 5.6.12.5. Printing Extra Gradients Sequentially
  • 5.6.13. Restarting TD-DFT Calculations
  • 5.6.14. Use of TD-DFT for the Calculation of X-ray Absorption Spectra
  • 5.6.15. Transient spectra
  • 5.6.16. Excited State Geometry Optimization
    • 5.6.16.1. Root Following Scheme for Difficult Cases
    • 5.6.16.2. Criteria to Follow IROOTs - starting from ORCA6
    • 5.6.16.3. Geometry Optimization of SOC States
  • 5.6.17. Potential Energy Surface Scans
    • 5.6.17.1. Potential Energy Surface Scans along Normal Coordinates
    • 5.6.17.2. Normal Mode Scan Calculations Between Different Structures
  • 5.6.18. Non-adiabatic coupling matrix elements
    • 5.6.18.1. NACMEs with built-in electron-translation factor
    • 5.6.18.2. Numerical non-adiabatic coupling matrix elements
  • 5.6.19. Keyword List
• 5.7. Excited States via ROCIS and ROCIS/DFT
  • 5.7.1. General Description
    • 5.7.1.1. General Spin ROCIS
    • 5.7.1.2. Original ROCIS Implementation
    • 5.7.1.3. ROCIS/DFT
    • 5.7.1.4. Resolution of the Identity
  • 5.7.2. Core PNO-ROCIS, PNO-ROCIS/DFT
  • 5.7.3. Transition Metal L-Edges with ROCIS or DFT/ROCIS
  • 5.7.4. Resonant Inelastic Scattering Spectroscopy
    • 5.7.4.1. General
    • 5.7.4.2. Processing the spectra with orca_mapspc
    • 5.7.4.3. Generating Cuts
  • 5.7.5. ROCIS Magnetic Properties
  • 5.7.6. Natural Transition Orbitals/ Natural Difference Orbitals
  • 5.7.7. Keyword List
• 5.8. Excited States via MCRPA
  • 5.8.1. General Description
  • 5.8.2. Analyzing Transitions
  • 5.8.3. Natural Transition Orbitals
  • 5.8.4. X-Ray Absorption Spectroscopy
  • 5.8.5. Computational Aspects
    • 5.8.5.1. Large Molecules
    • 5.8.5.2. Convergence
  • 5.8.6. Keyword List
• 5.9. Excited States via EOM-CCSD
  • 5.9.1. Theory
    • 5.9.1.1. Initial Guess
    • 5.9.1.2. Hamiltonian Construction
    • 5.9.1.3. Solution of the (Nonsymmetric) Eigenproblem
    • 5.9.1.4. Convergence, Restart, Preconditioning and Subspace Expansion
    • 5.9.1.5. Properties in the RHF EOM implementation
  • 5.9.2. General Use
    • 5.9.2.1. Capabilities
  • 5.9.3. Memory Management
  • 5.9.4. Some tips and tricks for EOM-CC calculation
  • 5.9.5. Full keyword list
• 5.10. Excited States via STEOM-CCSD
  • 5.10.1. General Description
  • 5.10.2. Selection of Active space
  • 5.10.3. Active space selection using TD-DFT densities
  • 5.10.4. Reliability of the Calculated Excitation Energy
  • 5.10.5. Removal of IP and EA states with double excitation character
  • 5.10.6. Transition and difference densities
  • 5.10.7. Properties
  • 5.10.8. Solvation (Experimental)
  • 5.10.9. Spin-Orbit Coupling (Experimental)
  • 5.10.10. Core excitation
  • 5.10.11. Transient absorption
• 5.11. Excited States via IH-FSMR-CCSD
  • 5.11.1. General Description
  • 5.11.2. Properties
  • 5.11.3. Solvation Correction
• 5.12. Excited States via PNO-based coupled cluster
  • 5.12.1. General Description
  • 5.12.2. Reference State Energy
  • 5.12.3. Use of Local Orbitals
  • 5.12.4. Some tips and tricks for bt-PNO calculations
• 5.13. Excited States via DLPNO-STEOM-CCSD
  • 5.13.1. PNO dressing (experimental keyword)
  • 5.13.2. Keywords from STEOM-CCSD
  • 5.13.3. Example
  • 5.13.4. Tips and Tricks
• 5.14. One Photon Spectroscopy
  • 5.14.1. General Description
  • 5.14.2. Light-matter interaction approaches
  • 5.14.3. Natural electric circular dichroism
  • 5.14.4. SOC and SSC corrected spectrum
  • 5.14.5. OPS full list of keywords
  • 5.14.6. Notes
• 5.15. Core-Level Spectroscopy with Coupled Cluster Methods
  • 5.15.1. Core-Ionization
  • 5.15.2. Core-Ionization (UHF)
  • 5.15.3. Core-Excitation
  • 5.15.4. Core-Excitation (UHF)
• 5.16. Simulation and Fit of Vibronic Structure in Electronic Spectra, Resonance Raman Excitation Profiles and Spectra with the orca_asa Program
  • 5.16.1. General Description of the Program
  • 5.16.2. Spectral Simulation Procedures: Input Structure and Model Parameters
    • 5.16.2.1. Example: Simple Mode
    • 5.16.2.2. Example: Modelling of Absorption and Fluorescence Spectra within the IMDHO Model
    • 5.16.2.3. Example: Modelling of Absorption and Fluorescence Spectra within the IMDHOFA Model
    • 5.16.2.4. Example: Modelling of Effective Broadening, Effective Stokes Shift and Temperature Effects in Absorption and Fluorescence Spectra within the IMDHO Model
    • 5.16.2.5. Example: Modelling of Absorption and Resonance Raman Spectra for the 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene
    • 5.16.2.6. Example: Modelling of Absorption Spectrum and Resonance Raman Profiles for the 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene
  • 5.16.3. Fitting of Experimental Spectra
    • 5.16.3.1. Example: Gauss-Fit of Absorption Spectrum
    • 5.16.3.2. Example: Fit of Absorption and Resonance Raman Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene
    • 5.16.3.3. Example: Single-Mode Fit of Absorption and Fluorescence Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_{2u}\) Transition in Tetracene
  • 5.16.4. Quantum-Chemically Assisted Simulations and Fits of Optical Bandshapes and Resonance Raman Intensities
    • 5.16.4.1. Example: Quantum-Chemically Assisted Analysis and Fit of the Absorption and Resonance Raman Spectra for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene
    • 5.16.4.2. Important Notes about Proper Comparison of Experimental and Quantum Chemically Calculated Resonance Raman Spectra
    • 5.16.4.3. Example: Normal Mode Scan Calculations of Model Parameters for 1-\(^1\)A\(_g\) \(\rightarrow\) 1-\(^1\)B\(_u\) Transition in trans-1,3,5-Hexatriene
• 5.17. Absorption and Fluorescence Bandshapes using ORCA_ASA
• 5.18. Vibrational Spectroscopy
  • 5.18.1. IR Spectra
  • 5.18.2. Overtones, Combination Bands and Near IR Spectra via NEARIR
    • 5.18.2.1. Overtones and Combination Bands
    • 5.18.2.2. Near IR Spectra
    • 5.18.2.3. Using Other Methods for the VPT2 Correction
  • 5.18.3. Vibrational Circular Dichroism (VCD) Spectra
  • 5.18.4. Raman Spectra
  • 5.18.5. Resonance Raman Spectra
  • 5.18.6. NRVS Spectra
  • 5.18.7. Animation of Vibrational Modes
  • 5.18.8. Isotope Shifts
• 5.19. Anharmonic Analysis and Vibrational Corrections using VPT2/GVPT2 and orca_vpt2
  • 5.19.1. Vibrational corrections of molecular properties using VPT2
• 5.20. Electrical Properties - Electric Moments and Polarizabilities
  • 5.20.1. Atomic Dipole Moment and Polarizabilities
  • 5.20.2. Elprop Keywords
• 5.21. Nuclear Magnetic Resonance (NMR) Parameters
  • 5.21.1. NMR Chemical Shifts
  • 5.21.2. NMR Spin-Spin Coupling Constants
  • 5.21.3. Simulating NMR Spectra
  • 5.21.4. Visualizing shielding tensors using orca_plot
  • 5.21.5. Nucleus-independent chemical shielding
  • 5.21.6. Shielding tensor orbital decomposition
  • 5.21.7. Treatment of Tau in Meta-GGA Functionals
  • 5.21.8. Cartesian Index Conventions for EPR and NMR Tensors
  • 5.21.9. Paramagnetic NMR Shielding Tensors
  • 5.21.10. Spin-rotation Constants
  • 5.21.11. EPRNMR - keywords for magnetic properties
• 5.22. Electron Paramagnetic Resonance (EPR) Parameters
  • 5.22.1. The g-Tensor
    • 5.22.1.1. Theory
    • 5.22.1.2. Basic usage
    • 5.22.1.3. Gauge origin treatment
    • 5.22.1.4. Keywords
  • 5.22.2. Hyperfine Coupling
    • 5.22.2.1. Theory
    • 5.22.2.2. Basic usage
    • 5.22.2.3. A note on basis sets
    • 5.22.2.4. Hyperfine Coupling Keywords
  • 5.22.3. Zero-Field Splitting
    • 5.22.3.1. Theory
    • 5.22.3.2. Basic usage
    • 5.22.3.3. Detailed theory of the coupled-perturbed formulation
    • 5.22.3.4. ZFS Keywords
• 5.23. MP2 Level Magnetic Properties
  • 5.23.1. Calculating Properties from Existing Densities
• 5.24. CASSCF Linear Response
  • 5.24.1. Introduction
  • 5.24.2. Technical Notes
  • 5.24.3. Basic Usage
  • 5.24.4. Troubleshooting
  • 5.24.5. Notes on Printing
  • 5.24.6. Keywords
• 5.25. Mössbauer Parameters
  • 5.25.1. Isomer Shift
  • 5.25.2. Quadrupole splitting
  • 5.25.3. Basic usage
  • 5.25.4. Keywords
• 5.26. The Spin-Orbit Coupling Operator
  • 5.26.1. Exclusion of Atomic Centers
  • 5.26.2. Simple Input Keywords
• 5.27. Broken-Symmetry Wavefunctions and Exchange Couplings
  • 5.27.1. Approximate Spin Projection Method
• 5.28. Decomposition of the Magnetic Exchange Coupling
• 5.29. Magnetic Properties Through Quasi Degenerate Perturbation Theory
  • 5.29.1. Quasi Degenerate Perturbation Theory (QDPT) in a nutshell
  • 5.29.2. Magnetic Properties Through the Effective Hamiltonian
  • 5.29.3. QDPT Keywords
  • 5.29.4. Organization of QDPT Magnetic Properties Computation
• 5.30. Magnetic Relaxation
  • 5.30.1. General description of the program.
  • 5.30.2. Computing magnetic relaxation times using Orca_Magrelax.
  • 5.30.3. Running Orca_Magrelax calculations in various modules
  • 5.30.4. Fixing common issues
  • 5.30.5. Magrelax Keywords
• 5.31. Simulation of (Magnetic) Circular Dichroism and Absorption Spectra
  • 5.31.1. General description of the program
  • 5.31.2. Running and analyzing MCD calculations in TDDFT module
  • 5.31.3. Running MCD calculations in other modules
  • 5.31.4. List of related keywords
• 5.32. Interface to SINGLE_ANISO Module
  • 5.32.1. General Description
  • 5.32.2. Running SINGLE_ANISO Calculations
  • 5.32.3. Reference List of CASSCF/ANISO Keywords
  • 5.32.4. How to cite
• 5.33. Interface to POLY_ANISO Module
  • 5.33.1. General Description
  • 5.33.2. Files
    • 5.33.2.1. Input Files
    • 5.33.2.2. Output Files
  • 5.33.3. List of Keywords
    • 5.33.3.1. Mandatory Keywords Defining the Calculation
    • 5.33.3.2. Keywords Defining the Magnetic Exchange Interactions
    • 5.33.3.3. Optional General Keywords to Control the Input
• 5.34. DeltaSCF
  • 5.34.1. Theory
    • 5.34.1.1. SOSCF L-SR1 method
    • 5.34.1.2. Generalized Mode Following
  • 5.34.2. Freeze-and-release strategy
  • 5.34.3. Input and examples
    • 5.34.3.1. First Example: HOMO-LUMO Excited State of Formaldehyde
    • 5.34.3.2. Core-ionized States
    • 5.34.3.3. Diabatic Couplings
    • 5.34.3.4. Generalized Mode Following
    • 5.34.3.5. Freeze-and-release strategy
  • 5.34.4. Full keyword list
• 5.35. Extended Transition State with Natural Orbitals for Chemical Valence (ETS-NOCV/EDA-NOCV)
  • 5.35.1. Running an EDA-NOCV analysis in ORCA
  • 5.35.2. EDA-NOCV Output File
  • 5.35.3. Visualization of deformation density contributions using orca_plot
  • 5.35.4. Dealing with fragments with ground state degeneracy
  • 5.35.5. EDA-NOCV and Double-Hybrid Functionals
  • 5.35.6. List of Related Keywords
• 5.36. Local Energy Decomposition
  • 5.36.1. Closed shell LED
    • 5.36.1.1. Basic Usage
    • 5.36.1.2. Example
  • 5.36.2. Example: LED analysis of intermolecular interactions
  • 5.36.3. Open shell LED
    • 5.36.3.1. Basic Usage
    • 5.36.3.2. Example
  • 5.36.4. Fragment-Pairwise Local Energy Decomposition
    • 5.36.4.1. Example
  • 5.36.5. COVALED
    • 5.36.5.1. Basic Usage
    • 5.36.5.2. Example
    • 5.36.5.3. Keywords
  • 5.36.6. Dispersion Interaction Density plot
  • 5.36.7. Automatic Fragmentation
  • 5.36.8. Additional Features, Defaults and List of Keywords
  • 5.36.9. Atomic Decomposition Methods
    • 5.36.9.1. Atomic Decomposition of London Dispersion Energy (ADLD(LED))
      • 5.36.9.1.1. Basic Usage
      • 5.36.9.1.2. Example
    • 5.36.9.2. Atomic Decomposition of Exchange (ADEX(LED))
      • 5.36.9.2.1. Basic Usage
      • 5.36.9.2.2. Example
    • 5.36.9.3. Keywords
• 5.37. The Hartree-Fock plus London Dispersion (HFLD) Method
  • 5.37.1. Basic Usage
  • 5.37.2. Example
  • 5.37.3. Combined HFLD/LED Analysis
    • 5.37.3.1. Example
  • 5.37.4. Keywords
• 5.38. ADLD(D): Atomic Decomposition of DFT-D London Dispersion Energy
  • 5.38.1. Theory
    • 5.38.1.1. Basic Usage
    • 5.38.1.2. Example
    • 5.38.1.3. Keywords
• 5.39. Static Ground State DFT (SGS-DFT)
  • 5.39.1. Suitability of SGS-DFT for X-ray Spectroscopy
  • 5.39.2. Summary of Cross Section Equations
  • 5.39.3. Orbitals, States, and Energies
  • 5.39.4. Non-Relativistic Treatment in 1-Electron Orbital Basis
  • 5.39.5. Inclusion of Relativistic Effects
  • 5.39.6. Computations of X-ray Spectroscopic Properties