Relativistic calculations of electric field gradients using the Douglas–Kroll method Irina Malkin a , Olga L. Malkina b , Vladimir G. Malkin b, * a Department of Theoretical Physics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynska dolina, Bratislava SK-84215, Slovakia b Institute of Inorganic Chemistry, Slovak Academy of Sciences, D ubravsk a cesta 9, Bratislava SK-84236, Slovakia Received 7 May 2002 Abstract In this work, the analytical evaluation of Douglas–Kroll (DK) transformed electric field gradient (EFG) integrals was implemented. This allowed us for the first time to perform fully analytical and picture-change consistent calcu- lations of nuclear quadrupole coupling constants in the framework of the DK method. Only scalar relativistic effects weretakenintoconsiderationinthepresentwork.Themethodwasappliedtothecalculationonaseriesofmoleculesat both Hartree–Fock and density functional levels of theory. The results were compared to the so-called point charge nuclear quadrupole model (PCNQM) numerical method. The results showed that, for the set of compounds investi- gated,thesecond-orderDKtransformationoftheEFGintegralsplaysonlyaminorroleincomparisonwiththefirst- order terms. Ó 2002 Elsevier Science B.V. All rights reserved. 1. Introduction The calculation of electric field gradients (EFGs) has received increased attention during pastfewyears[1–6].Oneofthereasonsistheop- portunity to use high-level quantum-chemical methods to determine nuclear quadrupole mo- ments (NQM) from experimental spectroscopic data [2–6]. Such calculations often give very reli- able results. However, since the EFG operator depends on the electron-nucleus distance r as r 3 , thispropertyisaffectedbyrelativisticeffectsmuch earlier than, for example, dipole moments or po- larizabilities. Thus for the accurate determination ofEFGsonheavynucleirelativisticeffectshaveto betakenintoaccount.Nowadayssuchcalculations are possible even with a four-component coupled cluster method [7]. Yet, they are still very de- manding computationally. As an alternative to four-component schemes different two-component approachesweresuggested[1,8].Theseapproaches were developed for the calculation of the total en- ergy of molecules. Their application to the calcu- lationofmolecularpropertiesisratherlimited,and relatively little experience is available [1,9]. The relativisticcalculationoftheEFG(whichisafirst- order property and still relatively straightforward tocalculate)thusappearstobeanattractivetarget. 30 July 2002 Chemical Physics Letters 361 (2002) 231–236 www.elsevier.com/locate/cplett * Corresponding author. Fax: +421-2-5941-0444. E-mail address: malkin@savba.sk (V.G. Malkin). 0009-2614/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII:S0009-2614(02)00956-9