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Discovering Chemistry
With Natural Bond
Orbitals
Discovering Chemistry
With Natural Bond
Orbitals
Frank Weinhold
Clark R. Landis
Theoretical Chemistry Institute
and Department of Chemistry
University of Wisconsin Madison
Wisconsin
Copyright Ó 2012 by John Wiley & Sons, Inc. All rights reserved
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
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10 9 8 7 6 5 4 3 2 1
The nature of the chemical bond is the problem at the heart
of all chemistry.
Bryce Crawford
Preface xi
1 Getting Started 1
1.1 Talking to your electronic structure system 1
1.2 Helpful tools 3
1.3 General $NBO keylist usage 4
1.4 Producing orbital imagery 6
Problems and exercises 8
2 Electrons in Atoms 10
3 Atoms in Molecules 34
3.1 Atomic orbitals in molecules 35
3.2 Atomic configurations and atomic charges in molecules 39
3.3 Atoms in open-shell molecules 44
Problems and exercises 49
vii
viii Contents
Index 309
Preface
xi
xii Preface
This book owes an obvious debt to Foresman and Frisch’s useful supplementary
manual, Exploring Chemistry with Electronic Structure Methods (2nd ed., Gaussian
Inc., Pittsburgh, PA, 1996), which provides an analogous how to guide for the popular
GaussianÔ electronic structure program. Combined with popular utilities such as
those made available on the WebMO website, the Gaussian program often makes
calculating a wavefunction as simple as a few mouse-clicks, and many such choices of
electronic structure system (ESS) are now widely available. The current Gaussian
version, Gaussian 09 (G09), is still the most widely used ESS in the chemical
literature, and it includes an elementary NBO module (the older “NBO 3.1” version)
that lets the student immediately perform many of the exercises described in this book.
However, the NBO program is indifferent to which ESS provided the wavefunction, or
even what type of wavefunction or density was provided, and the current book is
largely independent of such choices. For options that involve intricate interactions
with the host ESS and are implemented in only a select set of ESS packages, the
Gaussian/NBO form of input file will be used for illustrative purposes. However,
the present book has no specific association with the Gaussian program or the
Foresman–Frisch guidebook, and the only requirement is that the chosen host ESS
can pass wavefunction information to an NBO program (linked or stand-alone) that
allows the ESS wavefunction to be analyzed in chemically meaningful terms with the
help of the procedures and keywords described herein.
This book also serves as a complementary companion volume to the authors’
research monograph, Valency and Bonding: A Natural Bond Orbital Donor–
Acceptor Perspective (Cambridge University Press, 2005). The latter is theory- and
applications-dominated, offering little or no practical know-how for coaxing the NBO
program to yield the displayed numerical tables or graphical images. However, the
instructions and examples given in this book should allow the student to easily
reproduce any of the results given in Valency and Bonding, or to extend such treatment
to other chemical systems or higher levels of approximation. For complete consis-
tency with the numerical values and graphical orbital displays of Valency and
Bonding, we employ the same B3LYP/6-311 þþ G density functional theoretic
(DFT) methodology in this work. However, the student is encouraged to pursue
independent explorations of other computational methodologies (correlated or
uncorrelated, perturbative or variational, DFT or wavefunction-based, etc.) and other
chemical systems after mastering the illustrative examples of this book.
We thank Franklin Chen, Ken Fountain, John Harriman, J. R. Schmidt, Peter
Tentscher, and Mark Wendt for comments and suggestions on earlier drafts, with
special thanks to Mohamed Ayoub for reviewing Problems and Exercises throughout
the book.
We wish all readers of this book success on the path to discovery of enriched
chemical understanding from modern electronic structure calculations.
Figure 2.2 Fluorine atom (a) 2s, (b) 2p, and (c) 3d orbitals in 1D profile (left), 2D contour (middle), and
3D surface plot (right). The depicted orbitals have respective occupancies of 2, 1, and 0 in the F atom
ground state. (Note that the four outermost contour lines of default NBOView contour output do not include
the negative 2s “inner spike” near the nucleus, which is better seen in the 1D profile plot.)
Figure 4.1 Distinct valence (P)NBOs of HF of bonding (BD:sHF) and nonbonding type (LP: on-axis
F and off-axis nF ), shown in profile, contour, and surface plots. The profile of the py-type LP (NBO 4) is
n(s) (p)
along a vertical line through the F nucleus, perpendicular to the equivalent px-type LP (NBO 5, not shown)
that points out of the page.
Figure 4.5 sFH bond of hydrogen fluoride, shown as overlapping NHOs (upper) or as final NBO
(lower); (cf. I/O-4.7).
Figure 4.7 Lewis-type three-center tBHB bond of B2H6, showing contour plots for overlapping NHOs
(left) and final NBO (center), and corresponding surface plot (right).
Figure 5.2 Formamide nN and p*CO NBOs, shown individually (upper panels) and in interaction
(lower panels) as contour and surface plots. (The contour plot is a top–down view of the p system, with
chosen contour plane slicing through the p orbitals 1 Å above the molecular plane.)
Figure 5.4 Principal in-plane lone-pair ! antibond delocalizations of formamide, showing individual
ðyÞ
donor nO and acceptor s* CN ; s* CH NBOs (upper panels), and overlapping donor–acceptor pairs
(lower panels) in contour and surface plots.
Figure 5.5 Comparison contour and surface plots of vicinal sCH s* NH interactions in anti (upper)
versus syn (lower) orientations, showing the far more favorable NBO overlap in antiperiplanar
arrangement [consistent with the stronger hyperconjugative stabilization evaluated in the E(2) table].
Figure 5.9 Contour and surface plots comparing NBO (upper panels) and NLMO (lower panels) for
conjugatively delocalized amine lone pair nN [Eq. (5.42)] of formamide.
4 Chapter 1 Getting Started
research literature. Together with the documentation within the NBO source
code itself, the NBO Manual should be relied upon as the ultimate authority
on many points of details beyond the scope of the present book.
(2) The NBO website [www.chem.wisc.edu/nbo5] contains a variety of
important resources for both novice and accomplished NBO users,
including tutorials, interactive “self-explaining” output samples for all
major program options, FAQ (frequently asked questions), comprehensive
literature references to recent NBO applications, and much else. The NBO
website also contains program documentation for the NBOView orbital
viewer program that is used extensively throughout this book (see
Appendix B).
(3) The authors’ companion research monograph Valency and Bonding: A
Natural Bond Orbital Donor–Acceptor Perspective (Cambridge University
Press, Cambridge, 2005) describes applications of NBO analysis to a broad
variety of chemical problems spanning the periodic table. This monograph
also provides extensive theoretical background (V&B, Chapter 1) on the
physical and mathematical concepts that underlie NBO program options,
allowing the interested student to trace calculated NBO descriptors back to
fundamental quantum mechanical principles.
While the goal of this book is to facilitate the student’s entry into the ranks of
accomplished NBO users with minimal prerequisites or assumed background, we
shall freely include cross-references to NBO Manual pages, NBO website URLs, or
V&B content where appropriate.
The entryway to communication with your NBO program is the $NBO keylist, which
allows you to include desired keywords between initial $NBO and final $END
delimiters, namely,
Other NBO keylists to be described below (such as the $GENNBO . . . $END and
$COORD . . . $END keylists shown in I/O-1.1) are similarly opened by an identifying
$KEY identifier and closed by a matching $END delimiter, so it is important that these
delimiters be correctly located and spelled. A given keylist may extend over multiple
lines, for example,
$NBO
(chosen keywords)
$END
but no two keylists (or portions thereof) may occur on the same line. (In some non-
U.S. installations, the “$” identifier of keylist delimiters may be replaced by a more
convenient keyboard character.)
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4.
Hohlakovien luona
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Mutta heti kun Lise näki raosta Aljošan sormen, hän avasi oven
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Mullerrus vierashuoneessa