Evan J. Bieske

Spring constant calibration of atomic force microscope cantilevers of arbitrary shape

The spring constant of an atomic force microscope cantilever is often needed for quantitative measurements. The calibration method of Sader et al. [Rev. Sci. Instrum. 70, 3967 (1999)] for a rectangular cantilever requires measurement of the resonant frequency and quality factor in fluid (typically air), and knowledge of its plan view dimensions. This intrinsically uses the hydrodynamic function for a cantilever of rectangular plan view geometry. Here, we present hydrodynamic functions for a series of irregular and non-rectangular atomic force microscope cantilevers that are commonly used in practice. Cantilever geometries of arrow shape, small aspect ratio rectangular, quasi-rectangular, irregular rectangular, non-ideal trapezoidal cross sections, and V-shape are all studied. This enables the spring constants of all these cantilevers to be accurately and routinely determined through measurement of their resonant frequency and quality factor in fluid (such as air). An approximate formulation of the hydrodynamic function for microcantilevers of arbitrary geometry is also proposed. Implementation of the method and its performance in the presence of uncertainties and non-idealities is discussed, together with conversion factors for the static and dynamic spring constants of these cantilevers. These results are expected to be of particular value to the design and application of micro- and nanomechanical systems in general.

The infrared spectrum of the H2–HCO+ complex

A combined experimental and theoretical study of the structural properties of the H2–HCO+ ion‐neutral complex has been undertaken. Infrared vibrational predissociation spectra of mass selected H2–HCO+ complexes in the 2500–4200 cm−1 range display several vibrational bands, the most intense arising from excitation of the C–H and H2 stretch vibrations. The latter exhibits resolved rotational structure, being composed of Σ–Σ and Π–Π subbands as expected for a parallel transition of complex with a T‐shaped minimum energy geometry. The determined ground state molecular constants are in good agreement with ones obtained by ab initio calculations conducted at the QCISD(T)/6–311G(2df,2pd) level. The complex is composed of largely undistorted H2 and HCO+ subunits, has a T‐shaped minimum energy geometry with an H2...HCO+ intermolecular bondlength of approximately 1.75 A. Broadening of the higher J lines in the P and R branches of the Π–Π subband is proposed to be due to asymmetry type doubling, the magnitude of whi...

The 35Cl−–H2 and 35Cl−–D2 anion complexes: Infrared spectra and radial intermolecular potentials

Rotationally resolved mid-infrared spectra of the 35Cl−–H2 and 35Cl−–D2 anion complexes are measured in the regions associated with the H2 and D2 stretch vibrations. The 35Cl−–H2 spectrum contains a single Σ–Σ transition assigned to the more abundant ortho H2 containing species. The corresponding 35Cl−–D2 spectrum consists of two overlapping Σ–Σ transitions whose origins are separated by 0.24 cm−1, and which are due to absorptions by complexes containing para and ortho D2. The spectra are consistent with linear equilibrium structures for Cl−–H2 and Cl−–D2, although zero-point bending vibrational excursions are expected to be substantial. Ground state vibrationally averaged intermolecular separations between Cl− and the diatomic center-of-mass are deduced to be 3.195±0.003 A (35Cl−–H2) and 3.159±0.002 A (35Cl−–D2). Vibrational excitation of the diatomic core profoundly affects the intermolecular interaction and leads to contractions of 0.118 A (35Cl−–H2) and 0.078 A (35Cl−–D2) in the vibrationally averaged...

Mid‐infrared spectra of the proton‐bound complexes Nen–HCO+ (n=1,2)

The ν1 band of Ne–HCO+ has been recorded for both 20Ne and 22Ne containing isotopomers by means of infrared photodissociation spectroscopy. The rotational structure of the band is consistent with a parallel Σ–Σ type transition of a linear proton‐bound complex. The following constants are extracted for 20Ne–HCO+: ν0=3046.120±0.006 cm−1, B″=0.099 54±0.000 05 cm−1, D″=(5.30±0.30)×10−7 cm−1, H″=(1.1±0.9)×10−11 cm−1, B′=0.100 03±0.000 05 cm−1, D′=(4.89±0.30)×10−7 cm−1, H′=(1.6±0.9)×10−11 cm−1. The ν1 band is redshifted by 42.5 cm−1 from the corresponding ν1 transition of free HCO+ indicating that the Ne atom has a pronounced influence on the proton motion. Linewidths for individual rovibrational transitions are laser bandwidth limited, demonstrating that the lifetime of the ν1 level is at least 250 ps. An approximate radial potential for the collinear Ne...HCO+ interaction is constructed by joining the mid‐range potential obtained from a Rydberg–Klein–Rees inversion of the spectroscopic data to the theoretical...

Mid‐infrared spectra of He–HN+2 and He2–HN+2

Mid‐infrared vibrational spectra of He–HN+ 2 and He2–HN+ 2 have been recorded by monitoring their photofragmentation in a tandem mass spectrometer. For He–HN+ 2 three rotationally resolved bands are seen: the fundamental ν1 transition (N–H stretch) at 3158.419±0.009 cm−1, the ν1+ν b combination band (N–H stretch plus intermolecular bend) at 3254.671±0.050 cm−1, and the ν1+ν s combination band (N–H stretch plus intermolecular stretch) at 3321.466±0.050 cm−1. The spectroscopic data facilitate the development of approximate one‐dimensional radial intermolecular potentials relevant to the collinear bonding of He to HN+ 2 in its (000) and (100) vibrational states. These consist of a short range potential derived from an RKR inversion of the spectroscopic data, together with a long range polarization potential generated by considering the interaction between the He atom and a set of multipoles distributed on the HN+ 2 nuclei. The following estimates for binding energies are obtained: D 0 ″=378 cm−1 [He+HN+ 2(000)], and D 0 ′=431 cm−1 [He+HN+ 2(100)]. While the ν1 band of He2–HN+ 2 is not rotationally resolved, the fact that it is barely shifted from the corresponding band of He–HN+ 2 suggests that the trimer possesses a structure in which one of the He atoms occupies a linear proton‐bound position forming a He–HN+ 2 core, to which a second less strongly bound He is attached.

Dissociation energy of the ArHN+2 complex

The ArHN+2 ionic complex has been studied by means of infrared photodissociation spectroscopy in the region between 2470 and 6000 cm−1. The rotational constants for the ground state of the complex extracted from combination differences and B″ = 0.080862(15) cm−1 and D″ = 5.25(20) × 10−8 cm−1. For the transitions lying in the range 2470–2800 cm−1 predissociation could only be observed for rotational levels above a certain J′ value. This observation allows the binding energy of the complex to be determined as D0 = 2781.5 ± 1.5 cm−1.

The infrared spectrum of He–HCO+

The vibrational predissociationspectrum of the He–HCO+proton bound complex has been recorded in the 3 μm (C–H stretch) region by monitoring the HCO+ photofragment current. A rotationally resolved, parallel band is observed, red shifted 12.4 cm−1 from the ν1 transition of free HCO+. Analysis in terms of a diatomiclike Hamiltonian yields B″=0.2900±0.0002 cm−1, D″=(1.00±0.06)×10−5 cm−1, B′=0.2898±0.0010 cm−1, and ν1=3076.313±0.010 cm−1. Localized perturbations to ν1 rotational levels are observed and are tentatively ascribed to interactions with combination vibrational states made up of quanta of the CO stretch and HCO+ bend, and those of the low frequency intermolecular stretches and bends. Rotational linewidths are laser bandwidth limited suggesting a lower limit of approximately 250 ps for the lifetime of the ν1 level.

Ab initio potential energy and dipole moment surfaces, infrared spectra, and vibrational predissociation dynamics of the 35Cl−⋯H2/D2 complexes

Three-dimensional potential energy and dipole moment surfaces of the Cl−–H2 system are calculated ab initio by means of a coupled cluster method with single and double excitations and noniterative correction to triple excitations with augmented correlation consistent quadruple-zeta basis set supplemented with bond functions, and represented in analytical forms. Variational calculations of the energy levels up to the total angular momentum J=25 provide accurate estimations of the measured rotational spectroscopic constants of the ground van der Waals levels n=0 of the Cl−⋯H2/D2 complexes although they underestimate the red shifts of the mid-infrared spectra with v=0→v=1 vibrational excitation of the monomer. They also attest to the accuracy of effective radial interaction potentials extracted previously from experimental data using the rotational RKR procedure. Vibrational predissociation of the Cl−⋯H2/D2(v=1) complexes is shown to follow near-resonant vibrational-to-rotational energy transfer mechanism so...

Cl−–C6H6, Br−–C6H6, and I−–C6H6 anion complexes: Infrared spectra and ab initio calculations

Vibrational predissociation spectroscopy is used to obtain infrared spectra of the Cl−–C6H6, Br−–C6H6, and I−–C6H6 complexes in the region of the benzene CH stretch vibrations (2800–3200 cm−1). The infrared spectra of the three dimers are similar, each exhibiting several narrow bands (full width at half maximum <10 cm−1) that are only slightly redshifted from the absorptions of the free benzene molecule. Ab initio calculations predict that the most stable form of the three complexes is a planar C2v structure in which the halide is hydrogen bonded to two adjacent CH groups. The planar C2v structure in which the halide is linearly H bonded to a single CH group is predicted to be slightly less stable than the bifurcated form. Comparisons between experimental and theoretically predicted infrared spectra confirm that the bifurcated structure is indeed the most stable conformer for all three complexes. Ab initio calculations show that the electron density transfer from the halide to the benzene is not limited t...

Rotationally resolved infrared absorption spectrum of N+4

The rotationally resolved infrared band of the antisymmetric stretching vibration (ν3) of N+4 has been recorded by tunable diode laser spectroscopy. A continuous supersonic expansion of pure nitrogen through a slit nozzle and electron impact ionization was employed. Forty‐four P and R branch transitions with J up to 25 are observed. The band origin is at ν0=2234.5084(4) cm−1 and the rotational constants are determined to be B0=0.112 05(3) cm−1 and B1=0.111 76(3) cm−1. The infrared spectrum shows that N+4 has a linear ground state structure.