Bond! Chemical Bond: Electronic Structure Methods at Work
This chapter plunges into applied quantum chemistry , with various examples, ranging from elementary notions, up to rather advanced tricks of know-how and non-routine procedures of control and analysis.
In the first section, the first-principles power of the ab initio techniques is illustrated by a simple example of geometry optimization, starting from random atoms, ending with a structure close to the experimental data, within various computational settings (HF, MP2, CCSD, DFT with different functionals). Besides assessing the performances of the different methods, in mutual respects and facing the experiment, we emphasize the fact that the experimental data are affected themselves by limitations, which should be judged with critical caution. The ab initio outputs offer inner consistency of datasets, sometimes superior to the available experimental information, in areas affected by instrumental margins. In general, the calculations can retrieve the experimental data only with semi-quantitative or qualitative accuracy, but this is yet sufficient for meaningful insight in underlying mechanisms, guidelines to the interpretation of experiment, and even predictive prospection in the quest of properties design.
The second section focuses on HF and DFT calculations on the water molecule example, revealing the relationship with ionization potentials , electronegativity , and chemical hardness (electrorigidity) and hinting at non-routine input controls, such as the fractional tuning of populations in DFT (with the ADF code) or orbital reordering trick in HF (with the GAMESS program).
Keeping the H2O as play pool, the orbital shapes are discussed, first in the simple conjuncture of the Kohn–Sham outcome, followed by rather advanced technicalities in handling localized orbital bases, in a Valence Bond (VB) calculation, serving to extract a heuristic perspective on the hybridization scheme.
In a third section, the H2 example forms the background for discussing the bond as spin-coupling phenomenology, constructing the Heisenberg-Dirac-van Vleck (HDvV) effective spin Hamiltonian . In continuation, other calculation procedures, such as Complete Active Space Self-Consistent Field (CASSCF) versus Broken-Symmetry (BS) approach, are illustrated, in a hands-on style, with specific input examples, interpreting the results in terms of the HDvV model parameters, mining for physical meaning in the depths of methodologies.
The final section presents the Valence Bond (VB) as a valuable paradigm, both as a calculation technique and as meaningful phenomenology. It is the right way to guide the calculations along the terms of customary chemical language, retrieving the directed bonds, hybrid orbitals, lone pairs, and Lewis structures, in standalone or resonating status. The VB calculations on the prototypic benzene example are put in clear relation with the larger frame of the CASSCF method, identifying the VB-type states in the full spectrum and equating them in an HDvV modeling. The exposition is closed with a tutorial showing nice graphic rules to write down a phenomenological VB modeling, in a given basis of resonance structures . The recall of VB concepts in the light of the modern computational scene carries both heuristic and methodological virtues, satisfying equally well the goals of didacticism or of exploratory research. A brief excursion is taken into the domain of molecular dynamics problems, emphasizing the virtues of the vibronic coupling paradigm (the account of mutual interaction of vibration modes of the nuclei with electron movement) in describing large classes of phenomena, from stereochemistry to reactivity. Particularly, the instability and metastability triggered in certain circumstances by the vibronic coupling determines phase transitions of technological interest, such as the information processing. The vibronic paradigm is a large frame including effects known as Jahn–Teller and pseudo Jahn–Teller type, determining distortion of molecules from formally higher possible symmetries. We show how the vibronic concepts can be adjusted to the actual computation methods, using the so-called Coupled Perturbed frames designed to perform derivatives of a self-consistent Hamiltonian, with respect to different parametric perturbations. The vibronic coupling can be regarded as interaction between spectral terms, e.g. ground state computed with a given method and excited states taken at the time dependent (TS) version of the chosen procedure. At the same time, the coupling can be equivalently and conveniently formulated as orbital promotions, proposing here the concept of vibronic orbitals , as tools of heuristic meaning and precise technical definition, in the course of a vibronic analysis. The vibronic perspective, performed on ab initio grounds, allows clear insight into hidden dynamic mechanisms. At the same time, the vibronic modeling can be qualitatively used to classify different phenomena, such as mixed valence . It can be proven also as a powerful model Hamiltonian strategy with the aim of accurate fitting of potential energy surfaces of different sorts, showing good interpolation and extrapolation features and a sound phenomenological meaning.
Finally, within the symmetry breaking chemical field theory , the intriguing electronegativity and chemical hardness density functional dependencies are here reversely considered by means of the anharmonic chemical field potential, so inducing the manifested density of chemical bond in the correct ontological order: from the quantum field/operators to observable/measurable chemical field.
KeywordsComputational chemistry ab initio methods Hartree–Fock (HF) Density functional theory (DFT) Complete active space self consistent field (CASSCF) Valence bond (VB) Configuration interaction (CI) Electron correlation Quantum chemistry codes Gaussian General atomic and molecular electronic structure system (GAMESS) Amsterdam density functional (ADF) Input files Keyword controls Fractional occupation numbers Electronic density Electronegativity Chemical hardness (electrorigidity) Ionization potentials Spin coupling Heisenberg–Dirac–van Vleck (HDvV) spin hamiltonian Resonance structures Graphic rules for the VB phenomenological hamiltonian Vibronic coupling Jahn–Teller effect Pseudo Jahn–Teller effect Vibronic orbitals Coupled perturbed techniques Molecular dynamics Vibronic phenomenological models Mixed valence Potential energy surfaces Symmetry breaking Chemical field Electronic potential
- ADF2012.01, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam [http://www.scm.com]
- Atanasov M, Reinen D (2001) Density functional studies on the lone pair effect of the trivalent group (V) elements: I. electronic structure, vibronic coupling, and chemical criteria for the occurrence of lone pair distortions in AX3 molecules (A = N to Bi; X = H, and F to I). J Phys Chem A 105:5450–5467CrossRefGoogle Scholar
- Bode BM, Gordon MS (1998) Macmolplt: a graphical user interface for GAMESS. J Mol Graph Mod 16(3):133-138Google Scholar
- Cimpoesu F, Hirao K (2003) The ab initio analytical approach of vibronic quantities: application to inorganic stereochemistry. Adv Quant Chem 44:370–397Google Scholar
- Dirac, PAM (1978) Mathematical foundations of quantum theory. In: Marlow A (ed). Academic Press, New YorkGoogle Scholar
- Epstein ST (1974) The variation method in quantum chemistry. Academic Press, New YorkGoogle Scholar
- Flükiger P, Lüthi HP, Portmann S, Weber J (2000-2002) MOLEKEL version 4.3. Swiss Center for Scientific Computing, Manno (Switzerland)Google Scholar
- Fonseca Guerra C, Snijders JG, te Velde G, Baerends EJ (1998) Towards an order-N DFT method. Theor Chem Acc 99:391–403Google Scholar
- Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Montgomery JA Jr, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2009) Gaussian 09. Gaussian Inc, Wallingford CTGoogle Scholar
- Hwang C, Siegel DA, Mo SK, Regan W, Ismach A, Zhang Y, Zettl A, Lanzara A (2012) Fermi velocity engineering in graphene by substrate modification. Sci Rep 2:590/1–4Google Scholar
- Ishida S, Iwamoto T, Kabuto C, Kira M (2003) A stable silicon-based allene analogue with a formally sp-hybridized silicon atom. Nature 421 (6924):725-727Google Scholar
- Li J, Duke B, McWeeny R (2007) VB2000 Version 2.0, SciNet Technologies, San Diego, CAGoogle Scholar
- McWeeny R (2001) Methods of molecular quantum mechanics. Academic Press, LondonGoogle Scholar
- NIST (2015) National Institute for Science and Technology (NIST) on Constants, Units, and Uncertainty. http://physics.nist.gov/cuu/Constants/index.html
- Novoselov KS, Fal’ko VI, Colombo L, Gellert PR, Schwab MG, Kim K (2012) A roadmap for graphene. Nature 490:192–200Google Scholar
- Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Oxford University Press, New YorkGoogle Scholar
- Pauling L, Wheland GW (1933) The nature of the chemical bond. V. The quantum-mechanical calculation of the resonance energy of benzene and naphthalene and the hydrocarbon free radicals. J Chem Phys 1362Google Scholar
- Pulay P (1987) Analytical derivative methods in quantum chemistry. In: Lawley KP (ed) Ab Initio Methods in Quantum Chemistry. John Wiley, New YorkGoogle Scholar
- Putz MV (2008) The chemical bond: spontaneous symmetry-breaking approach. Symmetry: Cult Sci 19:249–262Google Scholar
- Putz MV (2016a) Quantum nanochemistry: a fully integrated approach. Vol 3: quantum molecules and reactivity. Apple Academic Press & CRC Press, TorontoGoogle Scholar
- Putz MV (2016b) Chemical field theory: the inverse density problem of electronegativity and chemical hardness for chemical bond. Curr Phys Chem 7(2):133-146. June 2017 doi: 10.2174/1877946806666160627101209
- Putz MV (2016c) Quantum nanochemistry: a fully integrated approach. Vol II: quantum atoms and periodicity. Apple Academic Press & CRC Press, TorontoGoogle Scholar
- Putz MV, Ori O, Diudea M, Szefler B, Pop R (2016) Bondonic chemistry: spontaneous symmetry breaking of the topo-reactivity on graphene. In: Ali Reza Ashrafi, Mircea V Diudea (eds) Chemistry and physics: distances, symmetry and topology in carbon nanomaterials. Springer, Dordrecht, pp 345–389Google Scholar
- Raimondi M, Cooper DL (1999) Ab initio modern valence bond theory. In: Surján PR, Bartlett RJ, Bogár F, Cooper DL, Kirtman B, Klopper W, Kutzelnigg W, March NH, Mezey PG, Müller H, Noga J, Paldus J, Pipek J, Raimondi M, Røeggen I, Sun JQ, Surján PR, Valdemoro C, Vogtner S (eds) Topics in current chemistry: localization and delocalization, vol 203. Reidel, Dordrecht, pp 105–120Google Scholar
- Sheka EF (2013) In: Hetokka M, Brandas E, Maruani J, Delgado-Barrio G (eds) Progress in theoretical chemistry and physics, vol 27, pp 249–284Google Scholar
- Song L, Chen Z, Ying F, Song J, Chen X, Su P, Mo Y, Zhang Q, Wu W (2012) XMVB 2.0: an ab initio non-orthogonal valence bond program. Xiamen University, Xiamen 361005, ChinaGoogle Scholar
- Walsh, AD (1953). The electronic orbitals, shapes, and spectra of polyatomic molecules. Part IV. Tetratomic hydride molecules, AH3. J Chem Soc 2296–2301Google Scholar
- Wolfram S (2003) The mathematica book, 5th edn. Wolfram-Media, Champaign, IllinoisGoogle Scholar
- Yamaguchi Y, Osamura Y, Goddard JD, Schaeffer H III (1994) A new dimension to quantum chemistry: analytic derivative methods in ab-initio molecular electronic structure theory. Oxford University Press, OxfordGoogle Scholar