Table Of ContentVOLUMEELEVEN
A R
NNUAL EPORTS IN
COMPUTATIONAL
CHEMISTRY
VOLUME ELEVEN
A R
NNUAL EPORTS IN
COMPUTATIONAL
CHEMISTRY
Edited by
DAVID A. DIXON
Department of Chemistry,
The University of Alabama,
Tuscaloosa, AL, USA
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON(cid:129)NEWYORK(cid:129)OXFORD
PARIS(cid:129)SANDIEGO(cid:129)SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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CONTRIBUTORS
JuanArago(cid:1)
InstitutodeCienciaMolecular,UniversidaddeValencia,Valencia,Spain
JochenAutschbach
DepartmentofChemistry,UniversityatBuffalo,StateUniversityofNewYork,Buffalo,
NY,USA
AttilaBende
MolecularandBiomolecularPhysicsDepartment,NationalInstituteforResearchand
DevelopmentofIsotopicandMolecularTechnologies,Cluj-Napoca,Romania
JoaquínCalbo
InstitutodeCienciaMolecular,UniversidaddeValencia,Valencia,Spain
ArnoutCeulemans
DepartmentofChemistry,KULeuven,Leuven,Belgium
AuroraE.Clark
DepartmentofChemistryandtheMaterialsScienceandEngineeringProgram,Washington
StateUniversity,Pullman,WA,USA
JulesTshishimbiMuya
DepartmentofChemistry,FacultyofScience,UniversityofKinshasa,Kinshasa,DRCongo;
DepartmentofChemistry,UniversityofRichmond,Richmond,VA,USA
MinhThoNguyen
DepartmentofChemistry,KULeuven,Leuven,Belgium
EnriqueOrtí
InstitutodeCienciaMolecular,UniversidaddeValencia,Valencia,Spain
JuanC.Sancho-García
DepartamentodeQuímicaFísica,UniversidaddeAlicante,Alicante,Spain
StefanoSimonucci
DepartmentofPhysics,UniversityofCamerino,Camerino,Italy;IstitutoNazionalediFisica
Nucleare,SezionediPerugia,Perugia,Italy
SimoneTaioli
EuropeanCentreforTheoreticalStudiesinNuclearPhysicsandRelatedAreas(ECT*),
BrunoKesslerFoundation&TrentoInstituteforFundamentalPhysicsandApplications
(TIFPA-INFN),Trento,Italy;FacultyofMathematicsandPhysics,CharlesUniversityin
Prague,Prague,CzechRepublic
j
ix
PREFACE
Annual Reports in Computational Chemistry provides reviews and/or
highlighted summaries of research areas relevant to computational
chemistry. The American Chemical Society’s Division of Computers in
Chemistry acted as editor for the first 10 volumes. Volume 11 is my first
volume as editor. A goal of the series is to provide reviews not only for
experts inthefieldbutalsoforstudentswho areinterested inlearninghow
to use computational methods to address real problems in chemistry.
Volume11hassixchapterswhicharefocusedonarangeofexcitingnew
computational chemistry developments ranging from scattering to the
predictionofpropertiestoanalyzingnetworksincomplexliquids.Itisnow
possible to measure the NMR chemical shifts and associated properties in
paramagnetic molecules and Chapter 1 (Quantum Chemistry Section)
describeshowtopredictthesevalues,openingupnewwaystointerpret,and
understand experimental data. Nonbonding interactions are critical in
chemistry, controlling many types of processes from catalytic reactions to
biochemicalprocessesandstructures.Althoughsuchweakinteractionshave
been the bane of density functional theory, new advances in exchange-
correlation functional have made it possible to properly capture these
interactions.Chapter2describestheuseofthenonlocalcorrelation density
functional VV10 to accurately capture noncovalent interactions. There is
substantialinterestintheuseoffemto-andattosecondlaserpulsestocontrol
chemistry and to observe electron-driven transformations such as bond
makingandbondbreakinginrealtime.Chapter3providesadescriptionof
how real-time time-dependent density functional theory can be used to
predict molecule–laser interactions and the associated dynamics of the
excited electrons. The final Chapter in Section A describes the use of
electronic structure calculations at the density functional theory level to
predictandunderstandthepropertiesofB ,anewinorganicfullerenebased
80
onboronwhichisthearchetypalboronbuckyball.Althoughsuchmolecules
havenotyetbeenobservedexperimentally,thisworkprovidesinsightsinto
these structures and how they differ from their carbon analogs as well as
providing unique insights into how solid boron may form from the gas.
Section B (Scattering) has one chapter on multichannel scattering theory
using Fano’s approach to the discrete–continuum interaction. This chapter
providesatheoreticalfoundationofthemethodanddiscussesabroadrange
of applications to molecules and solids from electron scattering to
j
xi
xii Preface
photoemission to nuclear chemistry. The final Section (Liquids) has one
chapter describing the development and use of Intermolecular Network
Theory as a general approach to understanding the structural and dynamic
properties of liquids. This method builds on a range of statistical mechanics
and computer science approaches such as PageRank, the Internet search
engine Google initially used to prioritize Web sites, to tackle the complex
problem of finding networks in dynamical simulations of liquids including
solutions.
Thisbookwouldnothavebeenpossiblewithoutthecontributionsfrom
the authors for which I am extremely grateful, including meeting a rather
tight schedule. This effort would also not have been successful without the
efforts of Shellie Bryant and Poppy Garraway from Elsevier to keep this
series going and helping me to develop a useful and quality volume in this
series. We hope that you will find this series useful and interesting. We are
currently working on Volume 12 and welcome contributions to it and
subsequentvolumes.Wewillexpandthesectionstoincludemorebranches
of computational chemistry. Do not hesitate to contact the editor with
suggestions for contributions or to volunteer providing a chapter.
Dr. DAVID A. DIXON, Editor
Robert Ramsay Chair
The University of Alabama
CHAPTERONE
NMR Calculations for
Paramagnetic Molecules
and Metal Complexes
Jochen Autschbach
DepartmentofChemistry,UniversityatBuffalo,StateUniversityofNewYork,Buffalo,NY,USA
E-mail:[email protected]
Contents
1. Introduction 3
2. Theory 5
3. pNMRChemicalShifts:SelectedCaseStudiesandOverviewofRecentlyPublished 17
ComputationalStudies
4. SummaryandOutlook 32
Acknowledgments 32
References 32
Abstract
Moleculesandmetalcomplexeswithparamagneticgroundstatesorlow-energypara-
magneticelectronicexcitedstatesmayexhibitprofoundeffectsduetoelectronpara-
magnetism on NMR parameters such as nuclear magnetic shielding constants and
indirect nuclear spinespin coupling. This review discusses different approaches that
can be used to calculate such effects from first principles, either with or without
employing fictitious spin Hamiltonian parameters. Case studies are presented, along
withanoverviewofselectedrecentlypublishedcomputationalstudiesofNMRchem-
icalshiftsofparamagneticsystems.
1. INTRODUCTION
Molecules and metal complexes with unpaired electrons may exhibit
pronounced electron paramagnetism. Such systems can be characterized
experimentally by exploiting the paramagnetism specifically, for instance
via measurements of the magnetic susceptibility or electron paramagnetic
resonance (EPR) spectra. Paramagnetic effects may also affect the nuclear
magnetic shielding tensors, the isotropic shielding, the chemical shifts, and
AnnualReportsinComputationalChemistry,Volume11
ISSN1574-1400 Copyright©2015ElsevierB.V. j
http://dx.doi.org/10.1016/bs.arcc.2015.09.006 Allrightsreserved. 3
4 JochenAutschbach
indirect nuclear spin-spin coupling (J-coupling), in nuclear magnetic reso-
nance(NMR)spectroscopy.TheacronympNMRisusedinhereininrefer-
enceto NMRofparamagneticsystems,ortheeffectson NMRparameters
thatare specific totheelectronparamagnetism.Ifthelatter leads totoofast
relaxation of the nuclear spins, it can be difficult to obtain NMR signals
experimentally. However, many experimental studies of paramagnetic spe-
cies reportdoften well resolveddNMR spectra where pNMR effects are
evident. Unfortunately, the interpretation and assignment of such spectra
canbechallenging.Consequently,thereisademandforquantumchemical
methodsandprotocolsthataresuitableforpredictingandanalyzingpNMR
data.
Norman Ramsey published the nonrelativistic theory for NMR shield-
ingfordiamagneticsystemsstartingin1950(1).Eightyearslater,McConnell
and Chesnut (2) derived the EPR spin Hamiltonian term that is bilinear in
thenuclearspinmagneticmomentandtheexternalmagneticfield,whichis
in essence the term responsible for the pNMR shift. This formulation has
been used for many pNMR chemical shift calculations ever since. In the
inorganic chemistry and organometallic chemistry communities, there are
also corresponding crystal-field (CF) theory based models for pNMR shifts
available (3e5) that remain in use. Previous derivations in terms of ab-initio
theory were put forward, for instance, by Kurland and McGarvey in 1970
(6), by Rinkevicius et al. (7) in 2003, and by Moon and Patchkovskii (8)
in 2004 who provided the first complete general theoretical formulation
and suggested a computational protocol in terms of EPR parameters. We
foregoadetailedhistoricalperspectiveoracomprehensiveaccountoftheo-
reticalmethodsthathavebeenproposedovertimeandtheirapplications.A
textbookchapterbyVaara(9)andtheMoonandPatchkovskiibookchapter
(8)covermuchoftherelevantolderliterature,andVaarasummarizesmany
ofthecomputationalstudiesavailableuptoca.2012.Thetheorysectionin
Vaara’sbookchapteremphasizesvariouscontributionstothepNMRshield-
ing tensor that can be defined in the leading order of relativistic effects,
which the reader might find instructive.
Recent years have witnessed redoubled efforts to establish reliable yet
practical theoretical approaches, which therefore warrants a short review.
We focus onchemicalshifts because pNMR effects on other NMRparam-
eters are essentially unexplored computationally, but an equation for
J-coupling is provided for completeness. As already pointed out, for a long
time, pNMR shifts have been expressed predominantly in terms of EPR
spin Hamiltonian parameters or spin susceptibilities, and calculations were
NMRCalculationsforParamagneticMoleculesandMetalComplexes 5
used to determine these quantities to estimate pNMR shifts. Only recently
has the focus shifted to what may be termed “direct” methods, i.e., calcula-
tions without recourse to EPR parameters or magnetic susceptibilities. We
taketheopportunitytooutlineaderivationbySonciniandVandenHeuvel
(SvH)(10,11),publishedin2013witha2012precursor(12),forthepNMR
shieldingtensorinanab-initioframeworkandhowtheEPRparameter-based
spinHamiltonianformulationisobtainedfromit.Werecentlyreportedthe,
to our knowledge, first direct ab-initio pNMR shift calculation (13). The
application to two actinide complexes also demonstrated that the SvH
formalism is compatible with a relativistic quantum chemistry framework
(14e16), which is crucial for systems with heavy elements.
Section2outlinesthetheory,andSection3discussesselectedcasestudies
utilizing EPR parameter- and magnetic susceptibility-based calculations as
well as the direct framework. Concluding remarks and an outlook can be
found in Section 4.
2. THEORY
We sketch the derivation by Soncini and Van den Heuvel (SvH) for
the nuclear magnetic shielding tensor as a temperature- (T-) dependent
bilinearderivativeoftheHelmholtzfreeenergy(10,11),usingthenotation
of a recent paper by our group (17).
The bilinear derivative of the Helmholtz free energy F is
v2F
sNðTÞ ¼ (1)
ij vBvmN
i j
Here,i,j˛{x,y,z},Nisthenucleusofinterest,mN isacomponentof
i
thenuclearspinmagneticmomentvectormN,andB isacomponentofthe
i
externalmagneticfieldvectorB.Thederivativesareunderstoodtobetaken
at B¼0, mN¼0. The result, sN, is a component of the nuclear magnetic
ij
shielding tensor sN in its Cartesian representation. The isotropic shielding
constant iss ¼(1/3)tr[s], where“tr” is thematrix trace (sum of diagonal
N
elements).
In a quantum mechanical framework, calculating a bilinear derivative
(a double-perturbation molecular property (18)) requires the linear and
b
bilinear derivatives of the Hamiltonian H:
b
HbHyF ¼ vH (2a)
Ni vmN
i
6 JochenAutschbach
b
HbZ ¼ vH (2b)
i vB
i
HbDS ¼ v2Hb (2c)
Nij vBvmN
i j
The term in Eqn (2a) is the hyperfine (HyF) operator component i
fornucleusNdescribingtheperturbationofthemoleculebythepresence
of the nuclear spin magnetic moment, Eqn (2b) is the electronic magnetic
moment operator component i describing the Zeeman (Z) interaction
with a static external magnetic field, and the bilinear derivative Eqn (2c)
is the diamagnetic shielding (DS) operator component i, j for nucleus N.
Note that SvH defined the operator linear in the external field explicitly
with a negative sign. Below, this would change the signs of the terms
that are bilinear in the first-order operators. (In Refs (13,17) we used a
similar notation as SvH but missed writing the negative sign in the
equation corresponding to Eqn (2b) in Ref. (17).) The electronic Hamil-
tonian in the absence of perturbations by the external field and the HyF
field is
X
Hb ¼ E jlaihlaj (3)
0 l
l;a
The normalized eigenfunctions jlai corresponding to the energies E
l
carry an index a to count the components of degenerate states. For conve-
nience, the components of a degenerate state are assumed to be mutually
orthogonal. SvH carried out a thermal average in the canonical ensemble
b
corresponding to H to arrive at the shielding tensor elements in a sum-
0
over-states (SOS) formulation:
"
X XD (cid:2) (cid:2) E
sNij ðTÞ ¼ Q1 e(cid:2)kEBlT la(cid:2)(cid:2)HbDNSij(cid:2)(cid:2)la
l aD (cid:2) (cid:2) ED (cid:2) (cid:2) E
(cid:2) (cid:2) (cid:2) (cid:2)
X X la(cid:2)HbZ(cid:2)l0a0 l0a0(cid:2)HbHyF(cid:2)la
i Nj
(cid:2)2Re (4)
l0sl a;a0 El0 (cid:2)El
#
XD (cid:2) (cid:2) ED (cid:2) (cid:2) E
(cid:2) 1 la(cid:2)(cid:2)HbZ(cid:2)(cid:2)la0 la0(cid:2)(cid:2)HbHyF(cid:2)(cid:2)la
k T i Nj
B a;a0
