Johan Lorentzon - Profile on Academia.edu (original) (raw)
Papers by Johan Lorentzon
This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, ... more This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, has treated the subject of fluid-structure interaction (FSI) for incompressible flow with small vibrations. The open source packages DEAL.II and OpenFOAM have been used to create a coupling between a finite element formulation for structure and a finite volume formulation for fluid (gas or liquid). A staggered solution algorithm for FSI has been implemented in C++ using Aitkens relaxation method together with a Reduced-Order-Model (ROM). The solution algorithm has been validated by using an application consisting of a cantilever immersed in a steady flow transversal to its axial direction. Also, vortex-induced vibrations (VIV) were calculated as a function of the flow velocity and successfully compared to empirical data. The study has demonstrated the usefulness of artifical damping to solve boundary condition problems in incompressible flow. The method presented is general and has a strong potential in technical applications where the structure is subjected to a surrounding fluid. To my supervisors, Johan Revstedt, Robert Zoltan Szasz, Per Erik Austrell: My thanks for being supportive in my work. To my friend Mathias Haage, I am truly grateful for your encouragement as consultant in the field of C++. The teachers Per Lidström, Matti Ristinmaa, Mathias Wallin, Claus Führer, Niels Saabye Ottosen and Jan Gustavsson my thanks for enduring my endless questions in the field of continuum mechanics and mathematics. I would also like to thank Gunnar Sparr, for the gift of the precious compendium "Kontinuerliga system" from year 1983, the very same version i lost on the train last year, a compendium that truly inspired me in my work. Finally, my thanks to my mentor Andrej Sadlev, for the years of fruitful discussions and meetings in the topic applied mathematics.
The influence of hydrodynamic damping on the motion of an immersed elastic cantilever
European Journal of Mechanics - B/Fluids
Dynamic response and wake structures of cantilevers with square cross-section
The dynamic response of cantilevers to a hydrodynamic load has been studied numerically. The Reyn... more The dynamic response of cantilevers to a hydrodynamic load has been studied numerically. The Reynolds number of the flow was fixed at 5000 and the variation in re-duced velocity was achieved by varying the Young’s modulus of the cantilever. Cantilevers with aspectratios of 5 and 10 were considered for reduced velocities in the range 2 to 30. The simulations were performed using a strongly coupled FSI tool based in the open source projects DEAL. IIand Open FOAM. The results show that as the eigenfrequency of the cantilever coincides with the vortex shedding frequency, the amplitude of the oscillation substantially increases, as expected. However, no desynchronization is observed for higher values of reduced velocity. Instead the amplitude remains fairly constant for the shorter cantilever and continuously increase for the longer one. (Less)
A numerical study of partitioned FSI applied to a cantilever in incompressible turbulent flow
International Journal for Numerical Methods in Engineering, 2019
This study presents an approach for partitioned fluid-structure interaction (FSI) applied to larg... more This study presents an approach for partitioned fluid-structure interaction (FSI) applied to large structural deformations, where an incompressible turbulent solver is combined with a structural solver. The implementation is based upon two different open-source libraries by using MPI as a parallel communication protocol, the packages and OpenFOAM. FSI is achieved through a strongly-coupled scheme. The solver has been validated against cases with a submerged cantilever in a channel flow to which experiments, numerical calculations and theoretical solutions are available. The verification of the procedure is performed by using a solid-solid interaction (SSI) study. The solver has proven to be robust and has the same parallel efficiency as the fluid and the solid solver stand-alone. (Less)
A study was performed on the passive control of Vortex-Induced Vibrations (VIV) for three differe... more A study was performed on the passive control of Vortex-Induced Vibrations (VIV) for three different geometric forms of cantilever twisted/taper/taper-twisted subjected to a turbulent flow. The method used is LES with dynamic Smagorinsky model, TVD spatial scheme and backward difference scheme in time. The results show a reduction of the drag coefficient (Cd) on mean by 5% and a reduction of the RMS of lift coefficient (Cl) by 50/80% for taper/twisted configuration, which is consistent with related studies. DMD analysis also show that the shear layer around the cantilever is desynchronized but further downstream it re-synchronize prior to the re-attachement point of the flow. This lead to a larger wake and street vortex with shape that reflects the deformation of the cantilever.
This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, ... more This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, has treated the subject of fluid-structure interaction (FSI) for incompressible flow with small vibrations. The open source packages DEAL.II and OpenFOAM have been used to create a coupling between a finite element formulation for structure and a finite volume formulation for fluid ( gas or liquid ). A staggered solution algorithm for FSI has been implemented in C++ using Aitkens relaxation method together with a Reduced-Order-Model (ROM). The solution algorithm has been validated by using an application consisting of a cantilever immersed in a steady flow transversal to its axial direction. Also, vortex-induced vibrations (VIV) were calculated as a function of the flow velocity and successfully compared to empirical data. The study has demonstrated the usefulness of artifical damping to solve boundary condition problems in incompressible flow. The method presented is general and has a s...
A numerical study of vortex-induced vibrations (viv) in an elastic cantilever
ChemInform Abstract: Ab initio Calculation of Inner-Sphere Reorganization Energies of Inorganic Redox Couples
ChemInform, 1993
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Theoretical Study of the Electronic Spectra of Uracil and Thymine
Journal of The American Chemical Society, 1995
Abstract: The complete active space (CAS) SCF method combined with multiconfigurational second-or... more Abstract: The complete active space (CAS) SCF method combined with multiconfigurational second-order perturbation theory has been used to study the electronic spectra-ie, vertical excitation energies, oscilator strengths, and transition moment directions-of the nucleic acid base ...
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzen... more ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest p ? p* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then ? p* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn ? p* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest π → π* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then → π* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn → π* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest p ? p* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then ? p* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn ? p* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
The ab initio calculation of inner sphere reorganization energies of inorganic redox couples
Journal of The American Chemical Society, 1993
... Reorganization energies, commonly denoted A, are important parameters in the Marcus theory of... more ... Reorganization energies, commonly denoted A, are important parameters in the Marcus theory of outer-sphere electron transfer.lS2 In simple terms, the reorganization energy represents the free energy increase associated with the structural changes of the reactants and their ...
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phe... more The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence ππ* state predicted by elementary π-electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm−1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzen... more ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.
This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, ... more This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, has treated the subject of fluid-structure interaction (FSI) for incompressible flow with small vibrations. The open source packages DEAL.II and OpenFOAM have been used to create a coupling between a finite element formulation for structure and a finite volume formulation for fluid (gas or liquid). A staggered solution algorithm for FSI has been implemented in C++ using Aitkens relaxation method together with a Reduced-Order-Model (ROM). The solution algorithm has been validated by using an application consisting of a cantilever immersed in a steady flow transversal to its axial direction. Also, vortex-induced vibrations (VIV) were calculated as a function of the flow velocity and successfully compared to empirical data. The study has demonstrated the usefulness of artifical damping to solve boundary condition problems in incompressible flow. The method presented is general and has a strong potential in technical applications where the structure is subjected to a surrounding fluid. To my supervisors, Johan Revstedt, Robert Zoltan Szasz, Per Erik Austrell: My thanks for being supportive in my work. To my friend Mathias Haage, I am truly grateful for your encouragement as consultant in the field of C++. The teachers Per Lidström, Matti Ristinmaa, Mathias Wallin, Claus Führer, Niels Saabye Ottosen and Jan Gustavsson my thanks for enduring my endless questions in the field of continuum mechanics and mathematics. I would also like to thank Gunnar Sparr, for the gift of the precious compendium "Kontinuerliga system" from year 1983, the very same version i lost on the train last year, a compendium that truly inspired me in my work. Finally, my thanks to my mentor Andrej Sadlev, for the years of fruitful discussions and meetings in the topic applied mathematics.
The influence of hydrodynamic damping on the motion of an immersed elastic cantilever
European Journal of Mechanics - B/Fluids
Dynamic response and wake structures of cantilevers with square cross-section
The dynamic response of cantilevers to a hydrodynamic load has been studied numerically. The Reyn... more The dynamic response of cantilevers to a hydrodynamic load has been studied numerically. The Reynolds number of the flow was fixed at 5000 and the variation in re-duced velocity was achieved by varying the Young’s modulus of the cantilever. Cantilevers with aspectratios of 5 and 10 were considered for reduced velocities in the range 2 to 30. The simulations were performed using a strongly coupled FSI tool based in the open source projects DEAL. IIand Open FOAM. The results show that as the eigenfrequency of the cantilever coincides with the vortex shedding frequency, the amplitude of the oscillation substantially increases, as expected. However, no desynchronization is observed for higher values of reduced velocity. Instead the amplitude remains fairly constant for the shorter cantilever and continuously increase for the longer one. (Less)
A numerical study of partitioned FSI applied to a cantilever in incompressible turbulent flow
International Journal for Numerical Methods in Engineering, 2019
This study presents an approach for partitioned fluid-structure interaction (FSI) applied to larg... more This study presents an approach for partitioned fluid-structure interaction (FSI) applied to large structural deformations, where an incompressible turbulent solver is combined with a structural solver. The implementation is based upon two different open-source libraries by using MPI as a parallel communication protocol, the packages and OpenFOAM. FSI is achieved through a strongly-coupled scheme. The solver has been validated against cases with a submerged cantilever in a channel flow to which experiments, numerical calculations and theoretical solutions are available. The verification of the procedure is performed by using a solid-solid interaction (SSI) study. The solver has proven to be robust and has the same parallel efficiency as the fluid and the solid solver stand-alone. (Less)
A study was performed on the passive control of Vortex-Induced Vibrations (VIV) for three differe... more A study was performed on the passive control of Vortex-Induced Vibrations (VIV) for three different geometric forms of cantilever twisted/taper/taper-twisted subjected to a turbulent flow. The method used is LES with dynamic Smagorinsky model, TVD spatial scheme and backward difference scheme in time. The results show a reduction of the drag coefficient (Cd) on mean by 5% and a reduction of the RMS of lift coefficient (Cl) by 50/80% for taper/twisted configuration, which is consistent with related studies. DMD analysis also show that the shear layer around the cantilever is desynchronized but further downstream it re-synchronize prior to the re-attachement point of the flow. This lead to a larger wake and street vortex with shape that reflects the deformation of the cantilever.
This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, ... more This Master Thesis in Technical Mathematics at LTH, directed towards simulation and computation, has treated the subject of fluid-structure interaction (FSI) for incompressible flow with small vibrations. The open source packages DEAL.II and OpenFOAM have been used to create a coupling between a finite element formulation for structure and a finite volume formulation for fluid ( gas or liquid ). A staggered solution algorithm for FSI has been implemented in C++ using Aitkens relaxation method together with a Reduced-Order-Model (ROM). The solution algorithm has been validated by using an application consisting of a cantilever immersed in a steady flow transversal to its axial direction. Also, vortex-induced vibrations (VIV) were calculated as a function of the flow velocity and successfully compared to empirical data. The study has demonstrated the usefulness of artifical damping to solve boundary condition problems in incompressible flow. The method presented is general and has a s...
A numerical study of vortex-induced vibrations (viv) in an elastic cantilever
ChemInform Abstract: Ab initio Calculation of Inner-Sphere Reorganization Energies of Inorganic Redox Couples
ChemInform, 1993
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Fluid-Structure Interaction (FSI) case study of a cantilever using OpenFOAM and DEAL. II with application to VIV
Theoretical Study of the Electronic Spectra of Uracil and Thymine
Journal of The American Chemical Society, 1995
Abstract: The complete active space (CAS) SCF method combined with multiconfigurational second-or... more Abstract: The complete active space (CAS) SCF method combined with multiconfigurational second-order perturbation theory has been used to study the electronic spectra-ie, vertical excitation energies, oscilator strengths, and transition moment directions-of the nucleic acid base ...
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzen... more ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest p ? p* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then ? p* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn ? p* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest π → π* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then → π* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn → π* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
A theoretical study of the electronic spectra of pyridine and phosphabenzene
Theoretical Chemistry Accounts, 1995
The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoreti... more The electronic excitation spectra of pyridine and phosphabenzene have been studied using theoretical methods. The electronic states are described by wave functions derived from second-order perturbation theory based on multiconfigurational reference functions. The study includes singlet and triplet valences excited states as well as a number of Rydberg states. For both molecules the transition energies to the two lowest p ? p* excited singlet states are known from experiment and reproduced with an accuracy of 0.15 eV or better, while then ? p* transition energies are predicted with a somewhat uncertain error of about 0.2 eV. The calculations suggest the lowestn ? p* transition detected experimentally in pyridine corresponds to an adiabatic transition. 43 electronic states have been determined in each of the molecules.
The ab initio calculation of inner sphere reorganization energies of inorganic redox couples
Journal of The American Chemical Society, 1993
... Reorganization energies, commonly denoted A, are important parameters in the Marcus theory of... more ... Reorganization energies, commonly denoted A, are important parameters in the Marcus theory of outer-sphere electron transfer.lS2 In simple terms, the reorganization energy represents the free energy increase associated with the structural changes of the reactants and their ...
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phe... more The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence ππ* state predicted by elementary π-electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm−1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.
A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol
Theoretical Chemistry Accounts, 1995
ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzen... more ABSTRACT The valence excited states and the 3s, 3p, and 3d (united atom) Rydberg states of benzene and phenol have been obtained by the CASPT2 method, which computes a second-order perturbation correction to complete active space self-consistent field (CASSCF) energies. All non-zero dipole oscillator strengths are also computed, at the CASSCF level. For benzene, 16 singlet and 16 triplet states with excitation energies up to ca. 7.86 eV (63 400 cm–1) are obtained. Of these, 12 singlet and three triplet energies are experimentally known well enough to allow meaningful comparison. The average error is around 0.1 eV. The highest of these singlet states (21 E2g) is the highest valence * state predicted by elementary -electron theory. Its energy is then considerably lower than has been suggested from laser flash experiments, but in perfect agreement with a reinterpretation of that experiment. For phenol, 27 singlet states are obtained, in the range 4.53–7.84 eV (63 300 cm–1). Only the lowest has a well-known experimental energy, which agrees with the computed result within 0.03 eV. The ionization energy is in error by 0.05 eV.