Search Menu
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information
Search Scholarly Publications

Title: Highly Accurate Prediction of Core Spectra of Molecules at Density Functional Theory Cost: Attaining Sub-electronvolt Error from a Restricted Open-Shell Kohn–Sham Approach

Journal Article · · Journal of Physical Chemistry Letters
ORCiD logo [1]; ORCiD logo [1]
  1. Univ. of California, Berkeley, CA (United States). Dept. of Chemistry, Kenneth S. Pitzer Center for Theoretical Chemistry; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Chemical Sciences Div.
+ Show Author Affiliations

We present the use of the recently developed square gradient minimization (SGM) algorithm for excited-state orbital optimization to obtain spin-pure restricted open-shell Kohn-Sham (ROKS) energies for core excited states of molecules. The SGM algorithm is robust against variational collapse and offers a reliable route to converging orbitals for target excited states at only 2-3 times the cost of ground-state orbital optimization (per iteration). ROKS/SGM with the modern SCAN/ωB97X-V functionals is found to predict the K-edge of C, N, O, and F to a root mean squared error of ~0.3 eV. ROKS/SGM is equally effective at predicting L-edge spectra of third period elements, provided a perturbative spin-orbit correction is employed. This high accuracy can be contrasted with traditional time-dependent density functional theory (TDDFT), which typically has greater than 10 eV error and requires translation of computed spectra to align with experiment. ROKS is computationally affordable (having the same scaling as ground-state DFT and a slightly larger prefactor) and can be applied to geometry optimizations/ab initio molecular dynamics of core excited states, as well as condensed phase simulations. ROKS can also model doubly excited/ionized states with one broken electron pair, which are beyond the ability of linear response based methods.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1779235
Journal Information:
Journal of Physical Chemistry Letters, Journal Name: Journal of Physical Chemistry Letters Journal Issue: 3 Vol. 11; ISSN 1948-7185
Publisher:
American Chemical SocietyCopyright Statement
Country of Publication:
United States
Language:
English

References (161)

Single-Reference ab initio Methods for the Calculation of Excited States of Large Molecules journal January 2006
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
Core-electron binding energies for gaseous atoms and molecules journal November 1984
Inner shell electron energy loss studies of HCN and C2N2 journal March 1979
Carbon K-shell excitation of C2H2, C2H4, C2H6 and C6H6 by 2.5 keV electron impact journal January 1977
An X-ray absorption study of glycine, methionine and proline journal March 2007
Theoretical approximations to X-ray absorption spectroscopy of liquid water and ice journal March 2010
A spin-restricted ensemble-referenced Kohn–Sham method and its application to diradicaloid situations journal May 1999
Ionization and fragmentation of OCS and CS2 after photoexcitation around the sulfur 2p edge journal August 1997
Photoinduced Structural Dynamics of Molecular Systems Mapped by Time-Resolved X-ray Methods journal May 2017
How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values journal March 2018
The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches journal October 2018
Reference Energies for Double Excitations journal January 2019
Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number journal October 2018
Photoinduced Heterocyclic Ring Opening of Furfural: Distinct Open-Chain Product Identification by Ultrafast X-ray Transient Absorption Spectroscopy journal September 2018
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory journal January 2015
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Excitation energies in density functional theory: An evaluation and a diagnostic test journal January 2008
Communication: Configuration interaction singles has a large systematic bias against charge-transfer states journal August 2011
On double vacancies in the core journal December 1986
Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold journal March 1998
Excitation energies and Stokes shifts from a restricted open-shell Kohn-Sham approach journal April 2013
Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states journal July 2018
Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional journal June 2018
Coupled cluster study of the x-ray absorption spectra of formaldehyde derivatives at the oxygen, carbon, and fluorine K-edges journal August 2019
K-shell excitation of HF and F 2 studied by electron energy-loss spectroscopy journal November 1981
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
K -shell photoabsorption of the N 2 molecule journal December 1989
High-resolution K -shell photoabsorption in formaldehyde journal October 1992
Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules journal February 2012
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Accurate absolute core-electron binding energies of molecules, solids, and surfaces from first-principles calculations journal October 2019
Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H$_2$ text January 2018
Efficient Simulation of Near-Edge X-ray Absorption Fine Structure (NEXAFS) in Density-Functional Theory: Comparison of Core-Level Constraining Approaches text January 2019
Excited state orbital optimization via minimizing the square of the gradient: General approach and application to singly and doubly excited states via density functional theory text January 2019
Calculating core-level excitations and x-ray absorption spectra of medium-sized closed-shell molecules with the algebraic-diagrammatic construction scheme for the polarization propagator journal August 2014
On the calculation of multiplet energies by the hartree-fock-slater method journal January 1977
Estimating the Hartree—Fock limit from finite basis set calculations journal June 2005
Direct SCF direct static-exchange calculations of electronic spectra
  • �gren, Hans; Carravetta, Vincenzo; Vahtras, Olav
  • Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta), Vol. 97, Issue 1-4 https://doi.org/10.1007/s002140050234
journal October 1997
Convergence acceleration of iterative sequences. the case of scf iteration journal July 1980
High resolution gas phase photoabsorption spectra of SiCl4 and Si(CH3)4 at the silicon l edges: characterization and assignment of resonances journal July 1987
A spin correction procedure for unrestricted Hartree-Fock and Møller-Plesset wavefunctions for singlet diradicals and polyradicals journal September 1988
Carbon and oxygen K-edge photoionization of the CO molecule journal September 1990
Core-electron binding energies for gaseous atoms and molecules journal November 1984
Inner shell electron energy loss studies of HCN and C2N2 journal March 1979
Inner shell and valence shell electronic excitation of ClF3 by high energy electron impact. An investigation of potential barrier effects journal October 1989
Nitrogen K-shell excitations in complex molecules and polypyrrole journal December 1995
Correlation of calculated and measured 2p spin-orbit splitting by electron spectroscopy using monochromatic x-radiation journal January 1974
Carbon K-shell excitation of C2H2, C2H4, C2H6 and C6H6 by 2.5 keV electron impact journal January 1977
Inner shell excitation and ionization of the monohalobenzenes journal January 1978
Fluorination effects on the inner-shell spectra of unsaturated molecules journal January 1988
High resolution gas phase photoabsorption spectra and multiple-scattering Xα study of PX3 (X=H, CH3, CF3) compounds at the P L2,3 edge journal September 1990
A spin-restricted ensemble-referenced Kohn–Sham method and its application to diradicaloid situations journal May 1999
Ionization and fragmentation of OCS and CS2 after photoexcitation around the sulfur 2p edge journal August 1997
Inner-shell excitation of PF3, PCl3, PCl2CF3, OPF3 and SPF3 journal November 1998
Relativistic corrections for single- and double-core excitation at the K- and L-edges from Li to Kr journal February 2017
Efficient implementation of core-excitation Bethe–Salpeter equation calculations journal December 2015
Self-interaction error of local density functionals for alkali–halide dissociation journal April 2006
Ti 1s pre-edge features in rutile: a Bethe-Salpeter calculation journal May 2004
An X-ray absorption study of glycine, methionine and proline journal March 2007
Theoretical approximations to X-ray absorption spectroscopy of liquid water and ice journal March 2010
ΔDFT/MIX: A reliable and efficient method for calculating core electron binding energies of large molecules journal August 2018
Ultrafast X-ray Transient Absorption Spectroscopy of Gas-Phase Photochemical Reactions: A New Universal Probe of Photoinduced Molecular Dynamics journal November 2018
Photoinduced Structural Dynamics of Molecular Systems Mapped by Time-Resolved X-ray Methods journal May 2017
Prediction of Excited-State Energies and Singlet–Triplet Gaps of Charge-Transfer States Using a Restricted Open-Shell Kohn–Sham Approach journal June 2016
How Accurate Is Density Functional Theory at Predicting Dipole Moments? An Assessment Using a New Database of 200 Benchmark Values journal March 2018
A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks journal June 2018
The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches journal October 2018
Probing Basis Set Requirements for Calculating Core Ionization and Core Excitation Spectroscopy by the Δ Self-Consistent-Field Approach journal November 2018
Reference Energies for Double Excitations journal January 2019
Non-Orthogonal Configuration Interaction with Single Substitutions for Core-Excited States: An Extension to Doublet Radicals journal April 2019
Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements journal July 2019
Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory journal February 2020
Delocalization Errors in Density Functional Theory Are Essentially Quadratic in Fractional Occupation Number journal October 2018
Tracing the 267 nm-Induced Radical Formation in Dimethyl Disulfide Using Time-Resolved X-ray Absorption Spectroscopy journal February 2019
Single-Reference ab Initio Methods for the Calculation of Excited States of Large Molecules journal November 2005
Experimental studies of the core excitation of imidazole, 4,5-dicyanoimidazole, and s-triazine journal July 1993
Photoinduced Heterocyclic Ring Opening of Furfural: Distinct Open-Chain Product Identification by Ultrafast X-ray Transient Absorption Spectroscopy journal September 2018
Near Edge X-ray Absorption Spectra of Some Small Polyatomic Molecules journal March 2003
Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM) † journal December 2008
Order and Orientation in Self-Assembled Long Chain Alkanephosphate Monolayers Adsorbed on Metal Oxide Surfaces journal October 2001
Simulation of X-ray absorption spectra with orthogonality constrained density functional theory journal January 2015
Molecular dynamics of NH 3 induced by core-electron excitation journal January 2015
A look at the density functional theory zoo with the advanced GMTKN55 database for general main group thermochemistry, kinetics and noncovalent interactions journal January 2017
How accurate are static polarizability predictions from density functional theory? An assessment over 132 species at equilibrium geometry journal January 2018
Beyond the Coulson–Fischer point: characterizing single excitation CI and TDDFT for excited states in single bond dissociations journal January 2019
On the determination of excitation energies using density functional theory journal January 2000
Time-dependent density functional theory calculations of near-edge X-ray absorption fine structure with short-range corrected functionals journal January 2009
Time-dependent density functional theory calculations of the spectroscopy of core electrons journal January 2010
ωB97X-V: A 10-parameter, range-separated hybrid, generalized gradient approximation density functional with nonlocal correlation, designed by a survival-of-the-fittest strategy journal January 2014
Core shell excitation of furan at the O1s and C1s edges: An experimental and ab initio study journal November 2003
Double excitations within time-dependent density functional theory linear response journal April 2004
Fragmentation dynamics of H2S following S 2p photoexcitation journal March 2005
High-resolution inner-shell excitation spectroscopy of H2-phthalocyanine journal July 2006
Spurious fractional charge on dissociated atoms: Pervasive and resilient self-interaction error of common density functionals journal November 2006
Many-electron self-interaction error in approximate density functionals journal November 2006
Are recent water models obtained by fitting diffraction data consistent with infrared/Raman and x-ray absorption spectra? journal December 2006
Excitation energies in density functional theory: An evaluation and a diagnostic test journal January 2008
A revised electronic Hessian for approximate time-dependent density functional theory journal November 2008
Self-consistent-field calculations of core excited states journal March 2009
Assessment of the ΔSCF density functional theory approach for electronic excitations in organic dyes journal February 2011
Electronic structure of GaInN semiconductors investigated by x-ray absorption spectroscopy journal May 2011
Communication: Configuration interaction singles has a large systematic bias against charge-transfer states journal August 2011
On double vacancies in the core journal December 1986
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties journal May 1993
Response functions in the CC3 iterative triple excitation model journal November 1995
Molecular excitation energies to high-lying bound states from time-dependent density-functional response theory: Characterization and correction of the time-dependent local density approximation ionization threshold journal March 1998
Toward reliable density functional methods without adjustable parameters: The PBE0 model journal April 1999
Excitation energies and Stokes shifts from a restricted open-shell Kohn-Sham approach journal April 2013
Mapping the genome of meta-generalized gradient approximation density functionals: The search for B97M-V journal February 2015
σ -SCF: A direct energy-targeting method to mean-field excited states journal December 2017
A theoretical and experimental benchmark study of core-excited states in nitrogen journal February 2018
Non-orthogonal configuration interaction with single substitutions for the calculation of core-excited states journal July 2018
Survival of the most transferable at the top of Jacob’s ladder: Defining and testing the ω B97M(2) double hybrid density functional journal June 2018
Communication: xDH double hybrid functionals can be qualitatively incorrect for non-equilibrium geometries: Dipole moment inversion and barriers to radical-radical association using XYG3 and XYGJ-OS journal May 2018
Communication: A mean field platform for excited state quantum chemistry journal August 2018
Well-behaved versus ill-behaved density functionals for single bond dissociation: Separating success from disaster functional by functional for stretched H 2 journal March 2019
Efficient simulation of near-edge x-ray absorption fine structure (NEXAFS) in density-functional theory: Comparison of core-level constraining approaches journal February 2019
Coupled cluster study of the x-ray absorption spectra of formaldehyde derivatives at the oxygen, carbon, and fluorine K-edges journal August 2019
A scaled CIS(D) based method for the calculation of valence and core electron ionization energies journal July 2019
The simulation of X-ray absorption spectra from ground and excited electronic states using core-valence separated DFT/MRCI journal October 2019
Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states journal December 2019
X-ray absorption spectroscopic investigation of the electronic structure differences in solution and crystalline oxyhemoglobin journal September 2013
A geometric approach to direct minimization journal June 2002
Conical intersections and double excitations in time-dependent density functional theory journal March 2006
Investigating excited electronic states using the algebraic diagrammatic construction (ADC) approach of the polarisation propagator journal February 2014
Advances in molecular quantum chemistry contained in the Q-Chem 4 program package journal September 2014
Overlapping core to valence and core to Rydberg transitions and resonances in the XUV spectra of SiF 4 journal January 1980
K-shell excitation of HF and F 2 studied by electron energy-loss spectroscopy journal November 1981
Vibrational structure of core to Rydberg state excitations of carbon dioxide and dinitrogen oxide journal January 1999
An x-ray absorption and a normal Auger study of the fine structure in the S2p −1 region of the CS 2 molecule journal April 2009
State-specific dissociation enhancement of ionic and excited neutral photofragments of gaseous CCl 4 and solid-state analogs following Cl 2p core-level excitation journal May 2008
Quantised Singularities in the Electromagnetic Field journal September 1931
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
A Relativistic Equation for Bound-State Problems journal December 1951
K -shell photoabsorption of the N 2 molecule journal December 1989
Decay channels of core-excited HCl journal June 1990
High-resolution K -shell photoabsorption in formaldehyde journal October 1992
K -shell excitation of the water, ammonia, and methane molecules using high-resolution photoabsorption spectroscopy journal February 1993
High-resolution measurements of near-edge resonances in the core-level photoionization spectra of SF 6 journal January 1993
Absorption by Some Molecular Gases in the Extreme Ultraviolet journal July 1972
Angle-resolved two-dimensional mapping of electron emission from the inner-shell 2 p excitations in Cl 2 journal May 2001
Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules journal February 2012
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Si L - and K -edge x-ray-absorption near-edge spectroscopy of gas-phase Si( CH 3 ) x ( OCH 3 ) 4 − x : Models for solid-state analogs journal November 1993
Bethe-Salpeter equation calculations of core excitation spectra journal March 2011
Evidence of Single-Photon Two-Site Core Double Ionization of C 2 H 2 Molecules journal November 2011
Experimental Verification of the Chemical Sensitivity of Two-Site Double Core-Hole States Formed by an X-Ray Free-Electron Laser journal April 2012
Single Photon K − 2 and K − 1 K − 1 Double Core Ionization in C 2 H 2 n ( n = 1 – 3 ), CO, and N 2 as a Potential New Tool for Chemical Analysis journal April 2013
Strongly Constrained and Appropriately Normed Semilocal Density Functional journal July 2015
Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy journal December 1982
Density-Functional Theory for Time-Dependent Systems journal March 1984
Generalized Gradient Approximation Made Simple journal October 1996
Accurate absolute core-electron binding energies of molecules, solids, and surfaces from first-principles calculations journal October 2019
Femtosecond x-ray spectroscopy of an electrocyclic ring-opening reaction journal April 2017
High-resolution gas phase P L-edge photoabsorption spectra of PF 5 journal October 2007
Time-Dependent Density Functional Response Theory for Molecules book November 1995
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space journal May 2008

Cited By (2)

An Overview of Self-Consistent Field Calculations Within Finite Basis Sets journal March 2020
An overview of self-consistent field calculations within finite basis sets text January 2019

Similar Records

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory
Journal Article · 2020 · Journal of Chemical Theory and Computation · OSTI ID:1779239
Computing x-ray absorption spectra from linear-response particles atop optimized holes
Journal Article · 2022 · Journal of Chemical Physics · OSTI ID:1878510
+1 more
Approximating Quasiparticle and Excitation Energies from Ground State Generalized Kohn–Sham Calculations
Journal Article · 2018 · Journal of Physical Chemistry. A, Molecules, Spectroscopy, Kinetics, Environment, and General Theory · OSTI ID:1566514
+1 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY