Physical Chemistry

"And, just like it should in all stories about philosophers, it ended up in complete chaos. In all their previous discussions they hadn't even asked themselves whether such a simple object as a brick, much less an electron, is an "essential object.""

"Three major sorts of infinities occur in quantum electrodynamics. The first, associated with the electron's infinite energy of interaction with its own electromagnetic field, is removed by redefining its mass to be the physical value, order by order, in perturbation theory. The second can be removed by demanding that a free electron produced at a given point in space be detectable with unit probability at some distant point at a later time. The third, related to the polarization of the vacuum pairs by a test charge, can be removed by redefining the electron's charge as its value as seen by a distant observer."

"The role of the Higgs interaction is remarkable — if electrons could not get mass via interacting with the Higgs field then atoms would be the size of the universe and our world could not exist. Further, when electrons do get mass via the interaction with the Higgs field, quantum corrections make them so massive they turn into black holes unless some new physics yet to be discovered allows them to be stabilized at their actual mass."

"Molecular dynamics is not primarily about making movies of molecules. More often it is about developing quantitative predictions of molecular size and shape, flexibilities, interactions with other molecules, behavior under pressure, and the relative frequency of one state or conformation compared to another. The complex nature of the force fields involved and the large size of typical molecular systems mean that molecular dynamics is almost always chaotic. The changes in a molecule that occur over time are important, but these should be understood in terms of changes in averaged quantities, structural forms, or families of “nearby” structures. Molecular dynamics relies on time-stepping to compute successive snapshots, but these are often used for sampling a probability distribution, or else a number of evolving paths are averaged to describe the likely sequence of changes that would be observed in a typical evolution of the molecule."

"Bond polarity is due to differences in electronegativity (EN), the intrinsic ability of an atom to attract the shared electrons in a covalent bond. As shown in Figure 2.2, electronegativities are based on an arbitrary scale, with fluorine the most electronegative (EN =4.0) and cesium the least (EN =0.7). Metals on the left side of the periodic table attract electrons weakly and have lower electronegativities, while oxygen, nitrogen, and halogens on the right side of the periodic table attract electrons strongly and have higher electronegativities. Carbon, the most important element in organic compounds, has an electronegativity value of 2.5.… As a rough guide, bonds between atoms whose electronegativities differ by less than 0.5 are nonpolar covalent, bonds between atoms whose electronegativities differ by 0.5–2 are polar covalent, and bonds between atoms whose electronegativities differ by more than 2 are largely ionic."

"Just as individual bonds are often polar, molecules as a whole are often polar also. Molecular polarity results from the vector summation of all individual bond polarities and lone-pair contributions in the molecule. As a practical matter, strongly polar substances are often soluble in polar solvents like water, whereas less polar substances are insoluble in water."

"Closely related to the ideas of bond polarity and dipole moment is the concept of assigning formal charges to specific atoms within a molecule, particularly atoms that have an apparently “abnormal” number of bonds. … Formal charges, as the name suggests, are a formalism and don’t imply the presence of actual ionic charges in a molecule. Instead, they’re a device for electron “bookkeeping” and can be thought of in the following way: a typical covalent bond is formed when each atom donates one electron. Although the bonding electrons are shared by both atoms, each atom can still be considered to “own” one electron for bookkeeping purposes."

"To express the calculations in a general way, the formal charge on an atom is equal to the number of valence electrons in a neutral, isolated atom minus the number of electrons owned by that bonded atom in a molecule. The number of electrons in the bonded atom, in turn, is equal to half the number of bonding electrons plus the nonbonding, lone-pair electrons."

"Most bonds, however, are neither fully ionic nor fully covalent but are somewhere between the two extremes. Such bonds are called polar covalent bonds, meaning that the bonding electrons are attracted more strongly by one atom than the other so that the electron distribution between atoms is not symmetrical."

"The lowest-energy arrangement, or ground-state electron configuration, of an atom is a listing of the orbitals occupied by its electrons. We can predict this arrangement by following three rules. Rule 1 The lowest-energy orbitals fill up first, according to the order 1s → 2s → 2p → 3s → 3p → 4s → 3d, a statement called the aufbau principle. Note that the 4sorbital lies between the 3pand 3dorbitals in energy. Rule 2 Electrons act in some ways as if they were spinning around an axis, somewhat as the earth spins. This spin can have two orientations, denoted as up (h) and down (g). Only two electrons can occupy an orbital, and they must be of opposite spin, a statement called the Pauli exclusion principle. Rule 3 If two or more empty orbitals of equal energy are available, one electron occupies each with spins parallel until all orbitals are half-full, a statement called Hund’s rule."

"We know through observation that eight electrons (an electron octet) in an atom’s outermost shell, or valence shell, impart special stability to the noble gas elements in group 8A of the periodic table."

"In the valence bond description, carbon uses hybrid orbitals to form bonds in organic molecules. When forming only single bonds with tetrahedral geometry, carbon uses four equivalent sp3 hybrid orbitals. When forming a double bond with planar geometry, carbon uses three equivalent sp2 hybrid orbitals and one unhybridized p orbital. When forming a triple bond with linear geometry, carbon uses two equivalent sp hybrid orbitals and two unhybridized p orbitals. Other atoms such as nitrogen, phosphorus, oxygen, and sulfur also use hybrid orbitals to form strong, oriented bonds."

"I was fortunate enough to hit on the focussing principle used in the mass spectrograph"

"It has long been known that the chemical atomic weight of hydrogen was greater than one-quarter of that of helium, but so long as fractional weights were general there was no particular need to explain this fact, nor could any definite conclusions be drawn from it."

"Since it is a close analogue of the ordinary spectrograph and gives a spectrum depending upon mass alone, the instrument is called a mass spectrograph and the spectrum it produces a mass spectrum."

"Should the research worker of the future discover some means of releasing this [atomic] energy in a form which could be employed, the human race will have at its command powers beyond the dreams of scientific fiction"

"We learned to make elephants fly."

"In small-molecule mass spectrometry, molecules are first ionized by collision with a high-energy electron beam. The ions then fragment into smaller pieces, which are magnetically sorted according to their mass-to-charge ratio (m/z). The ionized sample molecule is called the molecular ion, M1, and measurement of its mass gives the molecular weight of the sample. Structural clues about unknown samples can be obtained by interpreting the fragmentation pattern of the molecular ion. Mass-spectral fragmentations are usually complex, however, and interpretation is often difficult. In biological mass spectrometry, molecules are protonated using either electrospray ionization (ESI) or matrix-assisted laser desorption ionization (MALDI), and the protonated molecules are separated by time-of-flight (TOF)."

"I feel sure that there are many problems in Chemistry which could be solved with far greater ease by this than by any other method. The method is surprisingly sensitive — more so even than that of Spectrum Analysis, requires an infinitesimal amount of material, and does not require this to be specially purified: the technique is not difficult if appliances for high vacua are available."

"Nuclear magnetic resonance spectroscopy depends on the absorption of energy when the nucleus of an atom is excited from its lowest energy spin state to the next higher one. The nuclei of several elements can be studied by NMR. The two elements that are the most common in organic molecules (carbon and hydrogen) have isotopes (1H and 13C) capable of giving NMR spectra that are rich in structural information. A proton nuclear magnetic resonance (1H NMR) spectrum tells us about the environments of the various hydrogens in a molecule; a carbon-13 nuclear magnetic resonance (13C NMR) spectrum does the same for the carbon atoms. Separately and together 1H and 13C NMR take us a long way toward determining a substance’s molecular structure. We’ll develop most of the general principles of NMR by discussing 1H NMR, then extend them to 13C NMR. The 13C NMR discussion is shorter, not because it is less important than 1H NMR, but because many of the same principles apply to both techniques."

"In subsequent chapters, discussions regarding a number of nuclear magnetic resonance (NMR) techniques that could not be implemented when nuclear magnetic resonance was first discovered are presented. Their advent required, for example, strong magnetic fields and/or cryoprobes to accommodate limited sample availability. Pulsed field gradients (PFGs) have improved solvent suppression, have enabled efficient selective excitation, and have made accessible a different time range to diffusion coefficient measurement. Such developments have, of course, been made in parallel with increasing access to powerful computers and sophisticated software, permitting speedy processing and analysis of the various types and sizes of acquired data sets. Instrumental and software developments in the past 30 to 40 years have meant that NMR spectroscopy is now used in a wide range of scenarios. Synthetic chemists use NMR to elucidate structures of small molecules. It is employed in pharmaceutical industries for structure elucidation and drug development and screening (Chapter 3, Section 7.1). Biochemistry and biotechnology sectors utilise NMR to probe solution structures and functions of biological polymers (Chapter 7), and it is increasingly used in biomedicine (in particular, biomarker discovery; Chapter 6) for the analysis of complex matrices. Materials science (both soft and hard matters) is another application area in which solution and solid-state NMR has proved extremely valuable. While not an exhaustive list of applications, this is an illustration of the breadth of science that has benefitted from this analytical technique."

"The electron paramagnetic resonance discovered by Evgenii Konstantinovich is undoubtedly a first-class thing. It is a pity that nuclear magnetic resonance 'floated away'. Clearly, if Evgenii Konstantinovich had worked in better conditions, he would have done much more."

"In the absence of an external magnetic field, the spins of magnetic nuclei are oriented randomly. When a sample containing these nuclei is placed between the poles of a strong magnet, however, the nuclei adopt specific orientations, much as a compass needle orients in the earth’s magnetic field. A spinning 1H or 13C nucleus can orient so that its own tiny magnetic field is aligned either with (parallel to) or against (antiparallel to) the external field. The two orientations don’t have the same energy, however, and aren’t equally likely. The parallel orientation is slightly lower in energy by an amount that depends on the strength of the external field, making this spin state very slightly favored over the antiparallel orientation. ... If the oriented nuclei are irradiated with electromagnetic radiation of the proper frequency, energy absorption occurs and the lower-energy state “spinflips” to the higher-energy state. When this spin-flip occurs, the magnetic nuclei are said to be in resonance with the applied radiation—hence the name nuclear magnetic resonance."

"For magnetic fields that can be routinely produced in the laboratory, the transitions between energy levels for nuclear magnetic dipoles occur in the radio-frequency range, and the transitions between energy levels for unpaired electron spins occur in the microwave range. Nuclear magnetic resonance (NMR) and electron paramagnetic resonance (EPR) yield such valuable structural information that they have become indispensable in chemistry."

"The nuclei of certain elements, including 1H nuclei (protons) and 13C(carbon-13) nuclei, behave as though they were magnets spinning about an axis. When a compound containing protons or carbon-13 nuclei is placed in a very strong magnetic field and simultaneously irradiated with electromagnetic energy of the appropriate frequency, nuclei of the compound absorb energy through a process called magnetic resonance. The absorption of energy is quantized. ... We can use NMR spectra to provide valuable information about the structure of any molecule we might be studying. In the following sections we shall explain how four features of a molecule’s proton NMR spectrum can help us arrive at its structure."

"Back at Caltech, my research was going strong, and we had four different laboratories busy with experiments and people. In one of these laboratories, we were continuing with our work on coherence; in others, advancing techniques for shorter time resolution and for developing an optical analog for nuclear magnetic resonance (NMR). In NMR, the spin of nuclei with their transitions at radio frequencies is used for a variety of applications, ranging from the studies of molecular structure to magnetic resonance imaging (MRI), which is now commonly used in hospitals throughout the world."

"Catalysts are used in the production of a large variety of chemicals and fuels, as demonstrated by the fact that catalyst-based manufacturing accounts for about 60% of chemical products and 90% of processes (Senkan 2001). These numbers will likely increase in the future, considering all the advantages of a catalytic process: it requires only small amount of a ‘smart’ molecule to produce a large quantity of the desired compound; the catalyst usually allows operation under mild reaction conditions; also the economic benefits of an efficient catalytic process are enormous since it is less capital-intensive, has lower operating costs, produces products of higher purity and fewer by-products. In addition, catalysts provide important environmental benefits."

"Due to economic and ecological factors, catalytic processes in the production of fine chemicals are gaining in importance, especially in the area of asymmetric catalysis (Collins et al. 1997; Breuer et al. 2004). Accordingly, the practicing chemist has three major options: transition metal catalysts (Jacobsen et al. 1999), organocatalysts (Berkessel and Gröger 2004) or enzymes (Drauz and Waldmann 2002; Liese et al. 2006). All of them have advantages and disadvantages, which means that a given type of catalysis cannot be expected to provide general solutions to all problems of relevance in academic and industrial laboratories. Therefore, research in all three approaches needs to be intensified."

"If, as we yet can scarcely doubt, there are catalytic influences which are the cause of the miasmic spread of disease, it is possible that an antiseptic substance, such as , even in vanishingly small quantities, may indeed not be without definite influence upon such processes in the air. From daily and long continued spectrum observation it would be easy to learn whether the variation in the intensity of the spectral line Naα, produced by the sodium combination in the air, is related in any degree to the appearance and the spread of endemic diseases."

"How does electron sharing lead to bonding between atoms? Two models have been developed to describe covalent bonding: valence bond theory and molecular orbital theory. Each model has its strengths and weaknesses, and chemists tend to use them interchangeably depending on the circumstances. Valence bond theory is the more easily visualized of the two, so most of the descriptions we’ll use in this book derive from that approach."

"The behavior of a specific electron in an atom can be described by a mathematical expression called a wave equation—the same type of expression used to describe the motion of waves in a fluid. The solution to a wave equation is called a wave function, or orbital, and is denoted by the Greek letter psi (ψ). … What do orbitals look like? There are four different kinds of orbitals, denoted s, p, d,and f,each with a different shape. … The orbitals in an atom are organized into different electron shells, centered around the nucleus and having successively larger size and energy."

"The simplified treatment presented here has as its basis the theory of quantum mechanics developed independently in the 1920s by Heisenberg, Schrödinger, and Dirac. In this theory, the movement of an electron around a nucleus is expressed in the form of equations that are very similar to those characteristic of waves. The solutions to these equations, called atomic orbitals, allow us to describe the probability of finding the electron in a certain region in space. The shapes of these regions depend on the energy of the electron."

"The motion of electrons around the nucleus is described by wave equations. Their solutions, atomic orbitals, can be symbolically represented as regions in space, with each point given a positive, negative, or zero (at the node) numerical value, the square of which represents the probability of finding the electron there. The Aufbau principle allows us to assign electronic configurations to all atoms."

"Molecular orbital (MO) theory describes covalent bond formation as arising from a mathematical combination of atomic orbitals (wave functions) on different atoms to form molecular orbitals, so called because they belong to the entire molecule rather than to an individual atom. Just as an atomic orbital, whether unhybridized or hybridized, describes a region of space around an atom where an electron is likely to be found, so a molecular orbital describes a region of space in a molecule where electrons are most likely to be found."

"How do we construct H2 by using atomic orbitals? An answer to this question was developed by Pauling: Bonds are made by the in-phase overlap of atomic orbitals... The in-phase overlap of the two 1s orbitals results in a new orbital of lower energy called a bonding molecular orbital... On the other hand, out-of-phase overlap between the same two atomic orbitals results in a destabilizing interaction and formation of an antibonding molecular orbital."

"Atoms tend to form molecules in such a way as to reach an octet in the outer electron shell and attain a noble-gas configuration. … we describe two extreme ways in which this goal may be accomplished: by the formation of pure ionic or pure covalent bonds. … There are two extreme types of bonding, ionic and covalent. Both derive favorable energetics from Coulomb forces and the attainment of noble-gas electronic structures. Most bonds are better described as something between the two types: the polar covalent (or covalent ionic) bonds. … We thought of bonds in terms of Coulomb forces, then in terms of covalency and shared electron pairs, and now we have a quantum mechanical picture. Bonds are a result of the overlap of atomic orbitals. The two bonding electrons are placed in the bonding molecular orbital. Because it is stabilized relative to the two initial atomic orbitals, energy is given off during bond formation. This decrease in energy represents the bond strength."