Cited by 512

The DOI matches its Crossref record; 65 of the 65 references it cites were found in a registry or an index.

Relativistic Hamiltonians for Chemistry: A Primer

Open access

Saue, Trond·2011·ChemPhysChem

DOI 10.1002/cphc.201100682

Open this paper in CoChat — free account

Abstract

Entering Dirac territory: This Minireview provides a guide to two- and four-component relativistic Hamiltonians for use in quantum chemistry with particular emphasis on the recently developed eXact two-component (X2C) Hamiltonian.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Integrity signals

Registry

Crossref · 10.1002/cphc.201100682

Cites

65 of 65 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Relativistic regular two-component Hamiltonians
Lenthe, E. V., Baerends, E. J., & Snijders, J. G. (1993) · The Journal of Chemical Physics · doi:10.1063/1.466059 · Cited by 4,385
The quantum theory of the electron
Dirac, P. A. M. (1928) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1928.0023 · Cited by 3,657
Relativistic total energy using regular approximations
van Lenthe, E., Baerends, E. J., & Snijders, J. G. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467943 · Cited by 3,329
Relativistic effects in structural chemistry
Pyykko, P. (1988) · Chemical Reviews · doi:10.1021/cr00085a006 · Cited by 3,046
Quantum electrodynamical corrections to the fine structure of helium
Douglas, M., & Kroll, N. M. (1974) · Annals of Physics · doi:10.1016/0003-4916(74)90333-9 · Cited by 2,955
On the Dirac Theory of Spin 1/2 Particles and Its Non-Relativistic Limit
Foldy, L. L., & Wouthuysen, S. A. (1950) · Physical Review · doi:10.1103/physrev.78.29 · Cited by 2,183
A scale of directional substituent polarizability parameters from ab initio calculations of polarizability potentials
Hehre, W. J., Pau, C. F., Headley, A. D., Taft, R. W., & Topsom, R. D. (1986) · Journal of the American Chemical Society · doi:10.1021/ja00267a063 · Cited by 1,307
A mean-field spin-orbit method applicable to correlated wavefunctions
Heß, B. A., Marian, C. M., Wahlgren, U., & Gropen, O. (1996) · Chemical Physics Letters · doi:10.1016/0009-2614(96)00119-4 · Cited by 1,262
Quantum theory of cohesive properties of solids
Löwdin, P.-O. (1956) · Advances in Physics · doi:10.1080/00018735600101155 · Cited by 1,207
Molecular density functional calculations in the regular relativistic approximation: Method, application to coinage metal diatomics, hydrides, fluorides and chlorides, and comparison with first-order relativistic calculations
van Wüllen, C. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476576 · Cited by 989
The Effect of Retardation on the Interaction of Two Electrons
Breit, G. (1929) · Physical Review · doi:10.1103/physrev.34.553 · Cited by 860
DIRAC–FOCK ATOMIC ELECTRONIC STRUCTURE CALCULATIONS USING DIFFERENT NUCLEAR CHARGE DISTRIBUTIONS
Visscher, L., & Dyall, K. G. (1997) · Atomic Data and Nuclear Data Tables · doi:10.1006/adnd.1997.0751 · Cited by 826
Foundations of the relativistic theory of many-electron atoms
Sucher, J. (1980) · Physical Review A · doi:10.1103/physreva.22.348 · Cited by 824
The generalized Douglas–Kroll transformation
Wolf, A., Reiher, M., & Hess, B. A. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1515314 · Cited by 743
Regular Two-Component Pauli-Like Effective Hamiltonians in Dirac Theory
Chang, C., Pelissier, M., & Durand, P. (1986) · Physica Scripta · doi:10.1088/0031-8949/34/5/007 · Cited by 742
The quantum theory of the Electron. Part II
Dirac, P. A. M. (1928) · Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character · doi:10.1098/rspa.1928.0056 · Cited by 715
Introduction to Relativistic Quantum Chemistry
Dyall, K. G., & Faegri, K. (2007) · Oxford University Press eBooks · doi:10.1093/oso/9780195140866.001.0001 · Cited by 633
Exact decoupling of the Dirac Hamiltonian. II. The generalized Douglas–Kroll–Hess transformation up to arbitrary order
Reiher, M., & Wolf, A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1818681 · Cited by 605
An infinite-order two-component relativistic Hamiltonian by a simple one-step transformation
Iliaš, M., & Saue, T. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2436882 · Cited by 590
Self-citation
An exact separation of the spin-free and spin-dependent terms of the Dirac–Coulomb–Breit Hamiltonian
Dyall, K. G. (1994) · The Journal of Chemical Physics · doi:10.1063/1.466508 · Cited by 569
Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations
Stanton, R. E., & Havriliak, S. (1984) · The Journal of Chemical Physics · doi:10.1063/1.447865 · Cited by 568
Quasirelativistic theory equivalent to fully relativistic theory
Kutzelnigg, W., & Liu, W. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2137315 · Cited by 565
Nobel Lecture: Quantum chemical models
Pople, J. A. (1999) · Reviews of Modern Physics · doi:10.1103/revmodphys.71.1267 · Cited by 527
Nonrelativistic particles and wave equations
Lévy-Leblond, J.-M. (1967) · Communications in Mathematical Physics · doi:10.1007/bf01646020 · Cited by 527
On the interaction of two electrons
Brown, G. E., & Ravenhall, D. G. (1951) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1951.0181 · Cited by 520
Exact two-component Hamiltonians revisited
Liu, W., & Peng, D. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3159445 · Cited by 479
Interfacing relativistic and nonrelativistic methods. I. Normalized elimination of the small component in the modified Dirac equation
Dyall, K. G. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473860 · Cited by 423
Diagonalisation of the Dirac Hamiltonian as a basis for a relativistic many-body procedure
Heully, J. L., Lindgren, I., Lindroth, E., Lundqvist, S., & Martensson-Pendrill, A. M. (1986) · Journal of Physics B: Atomic and Molecular Physics · doi:10.1088/0022-3700/19/18/011 · Cited by 416
Basis set expansion of the dirac operator without variational collapse
Kutzelnigg, W. (1984) · International Journal of Quantum Chemistry · doi:10.1002/qua.560250112 · Cited by 350
Ideas of relativistic quantum chemistry
Liu, W. (2010) · Molecular Physics · doi:10.1080/00268971003781571 · Cited by 349
Relativistic Self-Consistent-Field Theory for Closed-Shell Atoms
Kim, Y. (1967) · Physical Review · doi:10.1103/physrev.154.17 · Cited by 348
LI. The dynamical motions of charged particles
Darwin, C. G. (1920) · The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786440508636066 · Cited by 336
Theory of relativistic effects on atoms: Configuration-space Hamiltonian
Mittleman, M. H. (1981) · Physical Review A · doi:10.1103/physreva.24.1167 · Cited by 317
Infinite-order two-component theory for relativistic quantum chemistry
Barysz, M., & Sadlej, A. J. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1436462 · Cited by 302
Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science
Reiher, M., & Wolf, A. (2009) · Wiley eBooks · doi:10.1002/9783527627486 · Cited by 296
Infinite-order quasirelativistic density functional method based on the exact matrix quasirelativistic theory
Liu, W., & Peng, D. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2222365 · Cited by 288
The interpretation of the new particles as displaced charge multiplets
Gell-Mann, M. (1956) · Il Nuovo Cimento · doi:10.1007/bf02748000 · Cited by 278
Making four- and two-component relativistic density functional methods fully equivalent based on the idea of “from atoms to molecule”
Peng, D., Liu, W., Xiao, Y., & Cheng, L. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2772856 · Cited by 264
A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac–Kohn–Sham equation
Komorovský, S., Repiský, M., Malkina, O. L., Malkin, V. G., Malkin Ondík, I., & Kaupp, M. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2837472 · Cited by 228
On the origin and contribution of the diamagnetic term in four-component relativistic calculations of magnetic properties
Aucar, G. A., Saue, T., Visscher, L., & Jensen, H. J. A. (1999) · The Journal of Chemical Physics · doi:10.1063/1.479181 · Cited by 214
Self-citation
Perturbation theory of relativistic corrections: 1. The non-relativistic limit of the Dirac equation and a direct perturbation expansion
Kutzelnigg, W. (1989) · Zeitschrift für Physik D Atoms, Molecules and Clusters · doi:10.1007/bf01436580 · Cited by 203
Relativistic calculations on the adsorption of CO on the (111) surfaces of Ni, Pd, and Pt within the zeroth-order regular approximation
Philipsen, P. H. T., van Lenthe, E., Snijders, J. G., & Baerends, E. J. (1997) · Physical Review B · doi:10.1103/physrevb.56.13556 · Cited by 188
Quasirelativistic theory. II. Theory at matrix level
Liu, W., & Kutzelnigg, W. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2710258 · Cited by 183
Relativistic and Quantum Electrodynamics Effects in the Helium Pair Potential
Przybytek, M., Cencek, W., Komasa, J., Łach, G., Jeziorski, B., & Szalewicz, K. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.183003 · Cited by 167
Relativistic regular approximations revisited: An infinite-order relativistic approximation
Dyall, K. G., & van Lenthe, E. (1999) · The Journal of Chemical Physics · doi:10.1063/1.479395 · Cited by 163
Relativistic atomic orbital contractions and expansions: magnitudes and explanations
Baerends, E. J., Schwarz, W. H. E., Schwerdtfeger, P., & Snijders, J. G. (1990) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/23/19/010 · Cited by 152
Approximate relativistic electronic structure methods based on the quaternion modified Dirac equation
Visscher, L., & Saue, T. (2000) · The Journal of Chemical Physics · doi:10.1063/1.1288371 · Cited by 151
Self-citation
Relativistic perturbation theory. I. A new perturbation approach to the Dirac equation
Rutkowski, A. (1986) · Journal of Physics B Atomic and Molecular Physics · doi:10.1088/0022-3700/19/2/005 · Cited by 150
Picture change and calculations of expectation values in approximate relativistic theories
Kellö, V., & Sadlej, A. J. (1998) · International Journal of Quantum Chemistry · doi:10.1002/(sici)1097-461x(1998)68:3<159::aid-qua3>3.0.co;2-u · Cited by 137
Quasirelativistic theory I. Theory in terms of a quasi-relativistic operator
Kutzelnigg, W., & Liu, W. (2006) · Molecular Physics · doi:10.1080/00268970600662481 · Cited by 122
Four-component relativistic theory for nuclear magnetic shielding constants: Critical assessments of different approaches
Xiao, Y., Liu, W., Cheng, L., & Peng, D. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2736702 · Cited by 92
Relativistic all-electron molecular Hartree-Fock-Dirac-(Breit) calculations on CH4, SiH4, GeH4, SnH4, PbH4
Visser, O., Visscher, L., Aerts, P. J. C., & Nieuwpoort, W. C. (1992) · Theoretical Chemistry Accounts · doi:10.1007/bf01134864 · Cited by 81
Matrix representation of the relativistic kinetic energy operator: Two-component variational procedure for the treatment of many-electron atoms and molecules
Buenker, R. J., Chandra, P., & Heß, B. A. (1984) · Chemical Physics · doi:10.1016/0301-0104(84)80001-4 · Cited by 76
Exact two-component relativistic theory for nuclear magnetic resonance parameters
Sun, Q., Liu, W., Xiao, Y., & Cheng, L. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3216471 · Cited by 68
Four-Component Electronic Structure Methods for Molecules
Saue, T., & Visscher, L. (2003) · Progress in theoretical chemistry and physics · doi:10.1007/978-94-017-0105-1_6 · Cited by 66
Self-citation
Comment on relativistic wave equations and negative-energy states
Heully, J., Lindgren, I., Lindroth, E., & Pendrill, A.-M. (1986) · Physical Review A · doi:10.1103/physreva.33.4426 · Cited by 62
Application of the complex-coordinate rotation to the relativistic Hylleraas-CI method: a case study
Pestka, G., Bylicki, M., & Karwowski, J. (2006) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/39/14/006 · Cited by 48
Spin-Interactions and the Non-relativistic Limit of Electrodynamics
Saue, T. (2005) · Advances in quantum chemistry · doi:10.1016/s0065-3276(05)48020-x · Cited by 45
Self-citation
Chapter 12 Perturbation theory of relativistic effects
Kutzelnigg, W. (2002) · Theoretical and computational chemistry · doi:10.1016/s1380-7323(02)80038-3 · Cited by 44
Effective Hamiltonians for degenerate and quasidegenerate direct perturbation theory of relativistic effects
Kutzelnigg, W. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478739 · Cited by 40
Analytic energy derivatives for regular approximations of relativistic effects applicable to methods with and without correlation corrections
Filatov, M. J., & Cremer, D. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1561046 · Cited by 36
A gauge-independent zeroth-order regular approximation to the exact relativistic Hamiltonian—Formulation and applications
Filatov, M. J., & Cremer, D. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1839856 · Cited by 35
Systematic treatment of relativistic effects accurate through arbitrarily high order in α2
Barysz, M. (2001) · The Journal of Chemical Physics · doi:10.1063/1.1370532 · Cited by 31
Effect of removing the no-virtual pair approximation on the correlation energy of the He isoelectronic sequence. II. Point nuclear charge model
Watanabe, Y., Nakano, H., & Tatewaki, H. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3359857 · Cited by 30
Effect of removing the no-virtual-pair approximation on the correlation energy of the He isoelectronic sequence
Watanabe, Y., Nakano, H., & Tatewaki, H. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2733647 · Cited by 29

Best‐Practice DFT Protocols for Basic Molecular Computational Chemistry**
Bursch, M., Mewes, J., Hansen, A., & Grimme, S. (2022) · Angewandte Chemie International Edition · doi:10.1002/anie.202205735 · Cited by 890

See all 512

Authors: Saue, T.
Venue: ChemPhysChem
Publisher: Wiley
Published: 2011-11-11
Volume: 12
Issue: 17
Pages: 3077-3094
ISSN: 1439-4235 (ISSN-L)
1439-7641
DOI: 10.1002/cphc.201100682
OpenAlex: W2123908305
Cited by: 512
References: 65
FWCI: 10.95
Type: journal article
Language: en
Open access: green

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.

Relativistic Hamiltonians for Chemistry: A Primer

Abstract

Overview

Integrity signals

Verification

Claims the paper makes

Self-check

Citations

Cites

Cited by

Metadata

Record

About these checks

Data sources