An update on the kilogram

We need a new definition for the kilogram! The present definition was sanctioned by the first General Conference on Weights and Measures (CGPM, Conférence Général des Poids et Mesures) in 1889, with a minor revision to the words in 1901, and remains unchanged after 116 years. It is the only base unit of the International System of Units (the SI) that is still defined in terms of a prototype artifact, the International Prototype of the Kilogram (IPK), which is kept in a safe at the International Bureau of Weights and Measures (the BIPM, Bureau International des Poids et Mesures) in Sèvres, near Paris.

On logarithmic ratio quantities and their units

The use of special units for logarithmic ratio quantities is reviewed. The neper is used with a natural logarithm (logarithm to the base e) to express the logarithm of the amplitude ratio of two pure sinusoidal signals, particularly in the context of linear systems where it is desired to represent the gain or loss in amplitude of a single-frequency signal between the input and output. The bel, and its more commonly used submultiple, the decibel, are used with a decadic logarithm (logarithm to the base 10) to measure the ratio of two power-like quantities, such as a mean square signal or a mean square sound pressure in acoustics. Thus two distinctly different quantities are involved. In this review we define the quantities first, without reference to the units, as is standard practice in any system of quantities and units. We show that two different definitions of the quantity power level, or logarithmic power ratio, are possible. We show that this leads to two different interpretations for the meaning and numerical values of the units bel and decibel. We review the question of which of these alternative definitions is actually used, or is used by implication, by workers in the field. Finally, we discuss the relative advantages of the alternative definitions.

Redefinition of the kilogram: a decision whose time has come

The kilogram, the base unit of mass in the International System of Units (SI), is defined as the mass m(K) of the international prototype of the kilogram. Clearly, this definition has the effect of fixing the value of m(K) to be one kilogram exactly. In this paper, we review the benefits that would accrue if the kilogram were redefined so as to fix the value of either the Planck constant h or the Avogadro constant NA instead of m(K), without waiting for the experiments to determine h or NA currently underway to reach their desired relative standard uncertainty of about 10−8. A significant reduction in the uncertainties of the SI values of many other fundamental constants would result from either of these new definitions, at the expense of making the mass m(K) of the international prototype a quantity whose value would have to be determined by experiment. However, by assigning a conventional value to m(K), the present highly precise worldwide uniformity of mass standards could still be retained. The advantages of redefining the kilogram immediately outweigh any apparent disadvantages, and we review the alternative forms that a new definition might take.

On defining base units in terms of fundamental constants

The definitions of the base units of the international system of units have been revised many times since the idea of such an international system was first conceived at the time of the French revolution. The objective today is to define all our units in terms of 'invariants of nature', i.e. by referencing our units to the fundamental constants of physics, or the properties of atoms, rather than the characteristics of our planet or of artefacts. This situation is reviewed, particularly in regard to finding a new definition of the kilogram to replace its present definition in terms of a prototype material artefact.

Amount of substance and the Mole

The International System of Units, the SI, is built upon seven base quantities and seven base units, as summarized in the table below. Although most of these are familiar to all scientists, the quantity “amount of substance” and its unit “mole” are less familiar and are mainly used by chemists.1 In the chemistry community, the unit “mole” is familiar, but the name of the corresponding quantity “amount of substance” is not so familiar, and the concept is still a source of difficulty for many students. This article reviews and clarifies these two concepts2 and discusses the definition of the unit “mole” and its possible revision.

The Bureau International des Poids et Mesures: establishing standards in the physical sciences

In a vault on the outskirts of Paris, a cylinder of platinum-iridium sits in a safe under three layers of glass. It is the kilogram, kept by the Bureau International des Poids et Mesures (BIPM), which is the international home of metrology. Metrology is the science of measurement, and it is of fundamental importance to us all. It is essential for trade, commerce, navigation, transport, communication, surveying, engineering, and construction. It is essential for medical diagnosis and treatment, health and safety, food and consumer protection, and for preserving the environment—e.g., measuring ozone in the atmosphere. Many of these applications are of particular relevance to chemistry and thus to IUPAC. In all these activities we need to make measurements reliably—to an appropriate and known level of uncertainty. The financial implications of metrology are enormous. In the United States, for example, some 15% of the gross domestic product is spent on healthcare, involving reliable quantitative measurements for both diagnosis and treatment.

Conventions for writing the values of quantities in the SI

Possible improvements to the conventional rules for using and writing the values of quantities in the International System of Units (SI) are discussed in the light of recent suggestions for improving the system with a view to making it more adaptable to use in computer codes.

Amount of substance and the proposed redefinition of the mole

There has been considerable discussion about the merits of redefining four of the base units of the SI, including the mole. In this paper, the options for implementing a new definition for the mole based on a fixed value for the Avogadro constant are discussed. They are placed in the context of the macroscopic nature of the quantity amount of substance and the opportunity to introduce a system for molar and atomic masses with unchanged values and consistent relative uncertainties.

Definitions of the units radian, neper, bel and decibel

The definition of coherent derived units in the International System of Units (SI) is reviewed, and the important role of the equations defining physical quantities is emphasized in obtaining coherent derived units. In the case of the dimensionless quantity plane angle, the choice between alternative definitions is considered, leading to a corresponding choice between alternative definitions of the coherent derived unit - the radian, degree or revolution. In this case the General Conference on Weights and Measures (CGPM) has chosen to adopt the definition that leads to the radian as the coherent derived unit in the SI. In the case of the quantity logarithmic decay (or gain), also sometimes called decrement, and sometimes called level, a similar choice of defining equation exists, leading to a corresponding choice for the coherent derived unit - the neper or the bel. In this case the CGPM has not yet made a choice. We argue that for the quantity logarithmic decay the most logical choice of defining equation is linked to that of the radian, and is that which leads to the neper as the corresponding coherent derived unit. This should not prevent us from using the bel and decibel as units of logarithmic decay. However, it is an important part of the SI to establish in a formal sense the equations defining physical quantities, and the corresponding coherent derived units.

Harmonic force fields from scaled SCF calculations: Program ASYM40

We report an extended version of our normal coordinate program ASYM40, which may be used to transform Cartesian force constants from ab initio calculations to a force field in nonredundant internal (symmetry) coordinates. When experimental data are available, scale factors for the theoretical force field may then be optimized by least-squares refinement. The alternative of refining an empirical force field to fit a wide variety of data, as with the previous version ASYM20, has been retained. We compare the results of least-squares refinement of the full harmonic force field with least-squares refinement of only the scale factors for an SCF calculated force field and conclude that the latter approach may be useful for large molecules where more sophisticated calculations are impractical. The refinement of scale factors for a theoretical force field is also useful when there are only limited spectroscopic data. The program will accept ab initio calculated force fields from any program that presents Cartesian force constants as output. The program is available through Quantum Chemistry Program Exchange.

Notations and conventions in molecular spectroscopy: part 1. General spectroscopic notation

The field of Molecular Spectroscopy was surveyed in order to determine a set of conventions and symbols which are in common use in the spectroscopic literature. This document, which is Part I in a series, establishes the notations and conventions used for general spectroscopic notations and deals with quantum mechanics, quantum numbers (vibrational states, angular momentum and energy levels), spectroscopic transitions, and miscellaneous notations (e.g. spectroscopic terms). Further parts will follow, dealing inter alia with symmetry notation, permutation and permutation-inversion symmetry notation, vibration-rotation spectroscopy and electronic spectroscopy.