Blair N McMaster | University of Canterbury/Te Whare Wānanga o Waitaha (original) (raw)

Papers by Blair N McMaster

Research paper thumbnail of An efficient algorithm for strongly focused optical beams propagating in Kerr media

Optics & Laser Technology, 2012

Abstract Due to the lens-induced quadratic phase factor from converging lens, the beam-propagatio... more Abstract Due to the lens-induced quadratic phase factor from converging lens, the beam-propagation method (BPM) is computationally expensive in simulations by the sampling theorem for lens-induced strongly focused beams propagating in nonlinear media. In the paper, we present a modified approach (MA) based on the separate envelope and lens-induced phase to only compute the envelope in the whole focal region. Then we demonstrate the correctness of MA analytically by the propagation of focused Gaussian beam and numerically by that of focused Super-Gaussian beam in linear media. Numerical simulations of strongly focused beams based on MA are in good agreement with those of BPM when propagating in Kerr media. The sampling requirement of MA which is similar with no lens-induced phase beam is lower than that of BPM which increases with the lens-induced chirp parameter and the propagation distance. Thus the computational efficiency can be greatly improved.

Research paper thumbnail of De que falamos quando falamos de framework na investigação em educação (matemática)?

Resumen Este artigo parte da necessidade de clarificação dos elementos constitutivos da investiga... more Resumen Este artigo parte da necessidade de clarificação dos elementos constitutivos da investigação em educação matemática. Em particular, discute-se o papel da teoria na investigação ea noção de framework teórico, prático e conceptual adoptando a ...

Research paper thumbnail of 从“苍蝇击倒冠军”说起

Research paper thumbnail of 1 Theory and Energetics of Mass Spectra

The quasi-equilibrium theory remains the cornerstone of discussions of mass spectral fragmentatio... more The quasi-equilibrium theory remains the cornerstone of discussions of mass spectral fragmentations in the literature, and has been well reviewed by Wahraftig.' However, very significant advances have been made in the theoretical treatments of chemical dynamics in closely related fields. More sophisticated experimental methods are now being applied to studies of ion decompositions and promise to fill some of the wide gaps in our knowledge. Most emphasis has been therefore placed on these aspects and a review style has been adopted, since this is felt to be more useful in the midst of such developments. Where clarification of concepts or methods seems necessary, criticism has been made in a spirit of stimulating further work and discussion. The topics reviewed follow a logical development. Theoretical calculations of ion structures and energies are briefly discussed, followed by ionization processes and their important relationship to energy deposition functions. Current developm...

Research paper thumbnail of Determination of electron impact ionization and appearance potentials

Journal of the Chemical Society, Chemical Communications, 1973

We show that a general formula may be applied to electron-impact ionization efficiency curves to ... more We show that a general formula may be applied to electron-impact ionization efficiency curves to determine the ionization or appearance potential of an ion without subjective assessment of ionization behaviour near threshold.

Research paper thumbnail of Analysis of Ionization Efficiency Curves

Advances in mass spectrometry

Research paper thumbnail of Theoretical Investigations of the Ammonium Radicals NH4, ND4 and NT4: Ground State Stability and Rydberg Transitions

Applied Quantum Chemistry, 1986

Research paper thumbnail of Acquisition of Ionization Efficiency data with conventional Ion Sources

Advances in mass spectrometry

Research paper thumbnail of Detritiation in 1,8-dimethylnaphthalene, acenaphthene and perinaphthane

Tetrahedron Letters, 1972

We reported recently' the rates of detritiation of 1,8_dimethylnaphthalene, acenaphthene and prri... more We reported recently' the rates of detritiation of 1,8_dimethylnaphthalene, acenaphthene and prrinaphthane in anhydro*Js trifluoroacetic acid at 30'.

Research paper thumbnail of LCAO local-spin-density and Xα calculations for Cr 2 and Mo 2

Molecular Physics, 1984

Broken-symmetry (C∞v) LCAO local-spin-density calculations using gaussian basis sets have been pe... more Broken-symmetry (C∞v) LCAO local-spin-density calculations using gaussian basis sets have been performed for Cr2 and Mo2 using five different approximations for the exchange and correlation potentials. The Xα potential is found to be inadequate. The correlated potentials of von Barth and Hedin, Gunnarsson and Lundqvist, Janak, Moruzzi and Williams, and Vosko, Wilk and Nusair all yield the same essential physics. The calculated bond lengths with these potentials are in near perfect agreement with experiment. The agreement for the dissociation energy is less good. The ‘best’ local potential (VWN) overestimates the binding energy by 55 per cent for Cr2 and 19 per cent for Mo2. The calculations indicate that Cr2 and Mo2 have equilibrium distances and binding energies which are close to those of a hypothetical hexuple bond, but vibrational properties which are drastically different. The large anharmonicities (and the proper dissociation of the molecules to high-spin atoms) are ultimately due to the rapid localization of the δ orbitals near Re, followed by a more gradual localization of the other orbitals as R increases. The electron spins are arranged in an antiferromagnetic fashion in these localized orbitals which yields the nearest possible one-electron (‘single determinant’) approximation to the observed Σ g ground state.

Research paper thumbnail of SCF-Xα-SW electron densities with the overlapping sphere approximation

Molecular Physics, 1982

Self consistent field-Xα-scattered wave (SCF-Xα-SW) calculations have been performed for a series... more Self consistent field-Xα-scattered wave (SCF-Xα-SW) calculations have been performed for a series of eight first and second row homonuclear diatomic molecules using both the touching (TS) and 25 per cent overlapping sphere (OS) versions. The OS deformation density maps exhibit much better quantitative agreement with those from other Xα methods, which do not employ the spherical muffin-tin (MT) potential approximation, than do the TS maps.The OS version thus compensates very effectively for the errors involved in the MT approximation in computing electron densities. A detailed comparison between the TS- and OS-Xα-SW orbitals reveals that the reasons for this improvement are surprisingly specific. The dominant effect of the OS approximation is to increase substantially the electron density near the midpoint of bonding σ orbitals, with a consequent reduction of the density behind the atoms. A similar effect occurs for the bonding π orbitals but is less pronounced. These effects are due to a change in hybridization of the orbitals, with the OS approximation increasing the proportion of the subdominant partial waves and hence changing the shapes of the orbitals. It is this increased orbital polarization which so effectively compensates for the lack of (non-spherically symmetric) polarization components in the MT potential, when overlapping spheres are used.

Research paper thumbnail of The stability and specrta of isotopic forms of the ammonium radical: An ab initio CI study of the dissociation barrier

Research paper thumbnail of Electronic structure of potassium clusters (K9, K15, K27) by the SCF X α(LSD) SW method

Chemical Physics, 1983

Spin-polarized self-consistent-field Xn sc~r~~rsd-~vave molecular-orbital calcularion~ have hccn ... more Spin-polarized self-consistent-field Xn sc~r~~rsd-~vave molecular-orbital calcularion~ have hccn performed fcrr clu~wr; i\f L). 15 and 27 potassium n~oms in the geometry of the hulk hi metal. Aa expected. this wricx ~IO~~~ a Awtx conwrptxxx ro~~xd~ the hulk (as measured by the bandwidth and ~hc density of SIZII~?;) than I~AI found in bimil;tr ztudie of zp I.-U) ;tnJ w.uwn,w mr1a1 clus~crs. For K,, a magnetic SI~I~ (n f = 10. #I 1 = 5) is found ox\ing IO rhe near dc~enerxy of Ihree eipenxaluez .n ~irc Fermi level. This points IO the need to consider the possibility of high-spin ZISWS in alkali clutters. The magnetic I~IIS psrkd for changes in the sphere radii. substitution of the Xn potential hy the local spin-dsnzity pownrial crf Gunnxzwn and Lundqvist and for a 20% reduction in the lattice parameter. However. a non-symmetric (D,, ) distortion L1~11n~~sd Ihe c\c's.r~ magnetism. yielding a state with only a sin_ele unpaired majority-spin rlecxon. II is wgge,~d thx the dcpendcncc of cIu2wr magnetism on structural parameters may lead IO ;L means of obtaining gsomerric inf~rrmakw h>-coupling s.tkul~rion~ af thiz t'pe with (future) Stern-Gerlnch measurements of the maprwic momems.

Research paper thumbnail of Theory and energetics of mass spectra

Mass Spectrometry, 1975

Ab initio Self-consistent Field Calculations including Electron Correlation.-An important distinc... more Ab initio Self-consistent Field Calculations including Electron Correlation.-An important distinction must be drawn between ab initio SCF calculations using extended basis sets and those using minimal basis Only the former are expected to give results of Hartree-Fock accuracy in the single-particle approximation (which ignores electron correlation). These calculations are very expensive for polyatomic molecules, and minimal basis set calculations are therefore more generally performed. With judicious choice of basis functions for particular systems, results within a few kcal mol-' of the Hartree-Fock limit can be obtained using minimal basis sets.5 But even with results of this accuracy erroneous conclusions may be drawn because electron correlation is ignored in the Hartree-Fock

Research paper thumbnail of CUTE-the design and evolution of a first year programming environment

… & Practice, 1998 …, 1998

A first Computer Science course should give students an appreciation of software engineering prin... more A first Computer Science course should give students an appreciation of software engineering principles and not merely teach programming skills in isolation. This is a difficult task, especially within the constraints imposed by a semester system. We report the evolution of the Canterbury University Teaching Environment (CUTE) which we have used successfully since 1993 to support our first-year programming courses. CUTE provides novice programmers with a simple graphical user interface (GUI) to important software development tools and services while shielding them from the underlying Unix system. This not only allows students to focus on core material within the constraints of the semester system but also simplifies administration.

Research paper thumbnail of An AB initio molecular orbital study of the ammonium radical

Chemical Physics, 1982

The 3s 'A, Rydberg ground statr of the ammonium radical. NH,, is predicted from UHF/UblP3 cnlculk... more The 3s 'A, Rydberg ground statr of the ammonium radical. NH,, is predicted from UHF/UblP3 cnlculkons using an rxtmsive basis set to have a tetrahedral geometry (r, = 1.02 A). but to undrrg~ dissociation by tunneling throqh a low barrier (5300 cm-I) IO Hi NH,. Dissociation paths to H 2 i NH2 (C,,. C,) wrrr also studird. bum no transition states of compwablg low energy were found. Trsnsiticn enrgies among the lowest Rydberg sutfcs were also dererminrd TLX termhrdral NH, and compared with Herzberg's recent assignment of the emission spectrum. with :tltrmativr assignments for the Sshhler hand being suggested.

Research paper thumbnail of Determination of electron impact ionization and appearance potentials

Journal of the Chemical Society, Chemical Communications, 1973

ABSTRACT We show that a general formula may be applied to electron-impact ionization efficiency c... more ABSTRACT We show that a general formula may be applied to electron-impact ionization efficiency curves to determine the ionization or appearance potential of an ion without subjective assessment of ionization behaviour near threshold.

Research paper thumbnail of Appearance potentials of metastable and normal ions and the kinetic shift

Journal of the Chemical Society, Chemical Communications, 1973

ABSTRACT Within experimental error, we could find no differences in the appearance potentials of ... more ABSTRACT Within experimental error, we could find no differences in the appearance potentials of corresponding metastable and normal ions in mass spectrometic decompositions of benzonitrile, benzene, and aniline and hence no evidence for any measurable kinetic shift.

Research paper thumbnail of Substituent effects in mass spectra of monosubstituted benzils

Organic Mass Spectrometry, 1975

ABSTRACT The mass spectra of a series of thirteen m- and p-substituted benzils have been determin... more ABSTRACT The mass spectra of a series of thirteen m- and p-substituted benzils have been determined at several ionising voltages below 20 eV and at 70 eV. At ionising voltages up to 5 eV above the ionisation potentials the benzil molecular ions decompose entirely by two pathways to give substituted and unsubstituted benzoyl ions. Fractional intensities of the molecular ion (FM), substituted (FX) and unsubstituted (FH) benzoyl ions were obtained for each benzil as a function of energy from measured ionisation efficiency curves, and ionisation and appearance potentials for all major ions determined from the ionisation efficiency curves by a semilogarithmic method. Various correlations of ion intensity and energy parameters with δ+ and δ constants are examined; these are generally poor. Fair correlations are obtained between log (FX/FH) or (AP – AP) and δ or δ+, and these are interpreted in terms of the expected effect of substituents on the stabilities of the product ions in the decompositions. A good correlation is observed between log (FX/FH) and AP · AP; this suggests that substituents affect FX/FH mainly by changing the activation energies for the competing decompositions of the molecular ions. The competitive shift has a marked effect on these appearance potentials so that in this system AP – IP is not a good measure of the activation energy for the primary decompositions.

Research paper thumbnail of An efficient algorithm for strongly focused optical beams propagating in Kerr media

Optics & Laser Technology, 2012

Abstract Due to the lens-induced quadratic phase factor from converging lens, the beam-propagatio... more Abstract Due to the lens-induced quadratic phase factor from converging lens, the beam-propagation method (BPM) is computationally expensive in simulations by the sampling theorem for lens-induced strongly focused beams propagating in nonlinear media. In the paper, we present a modified approach (MA) based on the separate envelope and lens-induced phase to only compute the envelope in the whole focal region. Then we demonstrate the correctness of MA analytically by the propagation of focused Gaussian beam and numerically by that of focused Super-Gaussian beam in linear media. Numerical simulations of strongly focused beams based on MA are in good agreement with those of BPM when propagating in Kerr media. The sampling requirement of MA which is similar with no lens-induced phase beam is lower than that of BPM which increases with the lens-induced chirp parameter and the propagation distance. Thus the computational efficiency can be greatly improved.

Research paper thumbnail of De que falamos quando falamos de framework na investigação em educação (matemática)?

Resumen Este artigo parte da necessidade de clarificação dos elementos constitutivos da investiga... more Resumen Este artigo parte da necessidade de clarificação dos elementos constitutivos da investigação em educação matemática. Em particular, discute-se o papel da teoria na investigação ea noção de framework teórico, prático e conceptual adoptando a ...

Research paper thumbnail of 从“苍蝇击倒冠军”说起

Research paper thumbnail of 1 Theory and Energetics of Mass Spectra

The quasi-equilibrium theory remains the cornerstone of discussions of mass spectral fragmentatio... more The quasi-equilibrium theory remains the cornerstone of discussions of mass spectral fragmentations in the literature, and has been well reviewed by Wahraftig.' However, very significant advances have been made in the theoretical treatments of chemical dynamics in closely related fields. More sophisticated experimental methods are now being applied to studies of ion decompositions and promise to fill some of the wide gaps in our knowledge. Most emphasis has been therefore placed on these aspects and a review style has been adopted, since this is felt to be more useful in the midst of such developments. Where clarification of concepts or methods seems necessary, criticism has been made in a spirit of stimulating further work and discussion. The topics reviewed follow a logical development. Theoretical calculations of ion structures and energies are briefly discussed, followed by ionization processes and their important relationship to energy deposition functions. Current developm...

Research paper thumbnail of Determination of electron impact ionization and appearance potentials

Journal of the Chemical Society, Chemical Communications, 1973

We show that a general formula may be applied to electron-impact ionization efficiency curves to ... more We show that a general formula may be applied to electron-impact ionization efficiency curves to determine the ionization or appearance potential of an ion without subjective assessment of ionization behaviour near threshold.

Research paper thumbnail of Analysis of Ionization Efficiency Curves

Advances in mass spectrometry

Research paper thumbnail of Theoretical Investigations of the Ammonium Radicals NH4, ND4 and NT4: Ground State Stability and Rydberg Transitions

Applied Quantum Chemistry, 1986

Research paper thumbnail of Acquisition of Ionization Efficiency data with conventional Ion Sources

Advances in mass spectrometry

Research paper thumbnail of Detritiation in 1,8-dimethylnaphthalene, acenaphthene and perinaphthane

Tetrahedron Letters, 1972

We reported recently' the rates of detritiation of 1,8_dimethylnaphthalene, acenaphthene and prri... more We reported recently' the rates of detritiation of 1,8_dimethylnaphthalene, acenaphthene and prrinaphthane in anhydro*Js trifluoroacetic acid at 30'.

Research paper thumbnail of LCAO local-spin-density and Xα calculations for Cr 2 and Mo 2

Molecular Physics, 1984

Broken-symmetry (C∞v) LCAO local-spin-density calculations using gaussian basis sets have been pe... more Broken-symmetry (C∞v) LCAO local-spin-density calculations using gaussian basis sets have been performed for Cr2 and Mo2 using five different approximations for the exchange and correlation potentials. The Xα potential is found to be inadequate. The correlated potentials of von Barth and Hedin, Gunnarsson and Lundqvist, Janak, Moruzzi and Williams, and Vosko, Wilk and Nusair all yield the same essential physics. The calculated bond lengths with these potentials are in near perfect agreement with experiment. The agreement for the dissociation energy is less good. The ‘best’ local potential (VWN) overestimates the binding energy by 55 per cent for Cr2 and 19 per cent for Mo2. The calculations indicate that Cr2 and Mo2 have equilibrium distances and binding energies which are close to those of a hypothetical hexuple bond, but vibrational properties which are drastically different. The large anharmonicities (and the proper dissociation of the molecules to high-spin atoms) are ultimately due to the rapid localization of the δ orbitals near Re, followed by a more gradual localization of the other orbitals as R increases. The electron spins are arranged in an antiferromagnetic fashion in these localized orbitals which yields the nearest possible one-electron (‘single determinant’) approximation to the observed Σ g ground state.

Research paper thumbnail of SCF-Xα-SW electron densities with the overlapping sphere approximation

Molecular Physics, 1982

Self consistent field-Xα-scattered wave (SCF-Xα-SW) calculations have been performed for a series... more Self consistent field-Xα-scattered wave (SCF-Xα-SW) calculations have been performed for a series of eight first and second row homonuclear diatomic molecules using both the touching (TS) and 25 per cent overlapping sphere (OS) versions. The OS deformation density maps exhibit much better quantitative agreement with those from other Xα methods, which do not employ the spherical muffin-tin (MT) potential approximation, than do the TS maps.The OS version thus compensates very effectively for the errors involved in the MT approximation in computing electron densities. A detailed comparison between the TS- and OS-Xα-SW orbitals reveals that the reasons for this improvement are surprisingly specific. The dominant effect of the OS approximation is to increase substantially the electron density near the midpoint of bonding σ orbitals, with a consequent reduction of the density behind the atoms. A similar effect occurs for the bonding π orbitals but is less pronounced. These effects are due to a change in hybridization of the orbitals, with the OS approximation increasing the proportion of the subdominant partial waves and hence changing the shapes of the orbitals. It is this increased orbital polarization which so effectively compensates for the lack of (non-spherically symmetric) polarization components in the MT potential, when overlapping spheres are used.

Research paper thumbnail of The stability and specrta of isotopic forms of the ammonium radical: An ab initio CI study of the dissociation barrier

Research paper thumbnail of Electronic structure of potassium clusters (K9, K15, K27) by the SCF X α(LSD) SW method

Chemical Physics, 1983

Spin-polarized self-consistent-field Xn sc~r~~rsd-~vave molecular-orbital calcularion~ have hccn ... more Spin-polarized self-consistent-field Xn sc~r~~rsd-~vave molecular-orbital calcularion~ have hccn performed fcrr clu~wr; i\f L). 15 and 27 potassium n~oms in the geometry of the hulk hi metal. Aa expected. this wricx ~IO~~~ a Awtx conwrptxxx ro~~xd~ the hulk (as measured by the bandwidth and ~hc density of SIZII~?;) than I~AI found in bimil;tr ztudie of zp I.-U) ;tnJ w.uwn,w mr1a1 clus~crs. For K,, a magnetic SI~I~ (n f = 10. #I 1 = 5) is found ox\ing IO rhe near dc~enerxy of Ihree eipenxaluez .n ~irc Fermi level. This points IO the need to consider the possibility of high-spin ZISWS in alkali clutters. The magnetic I~IIS psrkd for changes in the sphere radii. substitution of the Xn potential hy the local spin-dsnzity pownrial crf Gunnxzwn and Lundqvist and for a 20% reduction in the lattice parameter. However. a non-symmetric (D,, ) distortion L1~11n~~sd Ihe c\c's.r~ magnetism. yielding a state with only a sin_ele unpaired majority-spin rlecxon. II is wgge,~d thx the dcpendcncc of cIu2wr magnetism on structural parameters may lead IO ;L means of obtaining gsomerric inf~rrmakw h>-coupling s.tkul~rion~ af thiz t'pe with (future) Stern-Gerlnch measurements of the maprwic momems.

Research paper thumbnail of Theory and energetics of mass spectra

Mass Spectrometry, 1975

Ab initio Self-consistent Field Calculations including Electron Correlation.-An important distinc... more Ab initio Self-consistent Field Calculations including Electron Correlation.-An important distinction must be drawn between ab initio SCF calculations using extended basis sets and those using minimal basis Only the former are expected to give results of Hartree-Fock accuracy in the single-particle approximation (which ignores electron correlation). These calculations are very expensive for polyatomic molecules, and minimal basis set calculations are therefore more generally performed. With judicious choice of basis functions for particular systems, results within a few kcal mol-' of the Hartree-Fock limit can be obtained using minimal basis sets.5 But even with results of this accuracy erroneous conclusions may be drawn because electron correlation is ignored in the Hartree-Fock

Research paper thumbnail of CUTE-the design and evolution of a first year programming environment

… & Practice, 1998 …, 1998

A first Computer Science course should give students an appreciation of software engineering prin... more A first Computer Science course should give students an appreciation of software engineering principles and not merely teach programming skills in isolation. This is a difficult task, especially within the constraints imposed by a semester system. We report the evolution of the Canterbury University Teaching Environment (CUTE) which we have used successfully since 1993 to support our first-year programming courses. CUTE provides novice programmers with a simple graphical user interface (GUI) to important software development tools and services while shielding them from the underlying Unix system. This not only allows students to focus on core material within the constraints of the semester system but also simplifies administration.

Research paper thumbnail of An AB initio molecular orbital study of the ammonium radical

Chemical Physics, 1982

The 3s 'A, Rydberg ground statr of the ammonium radical. NH,, is predicted from UHF/UblP3 cnlculk... more The 3s 'A, Rydberg ground statr of the ammonium radical. NH,, is predicted from UHF/UblP3 cnlculkons using an rxtmsive basis set to have a tetrahedral geometry (r, = 1.02 A). but to undrrg~ dissociation by tunneling throqh a low barrier (5300 cm-I) IO Hi NH,. Dissociation paths to H 2 i NH2 (C,,. C,) wrrr also studird. bum no transition states of compwablg low energy were found. Trsnsiticn enrgies among the lowest Rydberg sutfcs were also dererminrd TLX termhrdral NH, and compared with Herzberg's recent assignment of the emission spectrum. with :tltrmativr assignments for the Sshhler hand being suggested.

Research paper thumbnail of Determination of electron impact ionization and appearance potentials

Journal of the Chemical Society, Chemical Communications, 1973

ABSTRACT We show that a general formula may be applied to electron-impact ionization efficiency c... more ABSTRACT We show that a general formula may be applied to electron-impact ionization efficiency curves to determine the ionization or appearance potential of an ion without subjective assessment of ionization behaviour near threshold.

Research paper thumbnail of Appearance potentials of metastable and normal ions and the kinetic shift

Journal of the Chemical Society, Chemical Communications, 1973

ABSTRACT Within experimental error, we could find no differences in the appearance potentials of ... more ABSTRACT Within experimental error, we could find no differences in the appearance potentials of corresponding metastable and normal ions in mass spectrometic decompositions of benzonitrile, benzene, and aniline and hence no evidence for any measurable kinetic shift.

Research paper thumbnail of Substituent effects in mass spectra of monosubstituted benzils

Organic Mass Spectrometry, 1975

ABSTRACT The mass spectra of a series of thirteen m- and p-substituted benzils have been determin... more ABSTRACT The mass spectra of a series of thirteen m- and p-substituted benzils have been determined at several ionising voltages below 20 eV and at 70 eV. At ionising voltages up to 5 eV above the ionisation potentials the benzil molecular ions decompose entirely by two pathways to give substituted and unsubstituted benzoyl ions. Fractional intensities of the molecular ion (FM), substituted (FX) and unsubstituted (FH) benzoyl ions were obtained for each benzil as a function of energy from measured ionisation efficiency curves, and ionisation and appearance potentials for all major ions determined from the ionisation efficiency curves by a semilogarithmic method. Various correlations of ion intensity and energy parameters with δ+ and δ constants are examined; these are generally poor. Fair correlations are obtained between log (FX/FH) or (AP – AP) and δ or δ+, and these are interpreted in terms of the expected effect of substituents on the stabilities of the product ions in the decompositions. A good correlation is observed between log (FX/FH) and AP · AP; this suggests that substituents affect FX/FH mainly by changing the activation energies for the competing decompositions of the molecular ions. The competitive shift has a marked effect on these appearance potentials so that in this system AP – IP is not a good measure of the activation energy for the primary decompositions.