Atomic and molecular systems are often intuitively separated into almost independent subsystems as, for example, the core and valence parts of an atom. Consequently, if this separation provides a good approximation, one can obtain the states of the system from the states of the subsystems which best represent the entire system. In the light of the work of McWeeny, in which one assumes strong orthogonality among subsystem wavefunctions, we determine an effective Hamiltonian for a given subsystem which should properly describe the states of that subsystem. Previous work is shown to have dealt with an improper effective Hamiltonian.

Several ink dating methods based on solvents analysis using gas chromatography/mass spectrometry (GC/MS) were proposed in the last decades. These methods follow the drying of solvents from ballpoint pen inks on paper and seem very promising. However, several questions arose over the last few years among questioned documents examiners regarding the transparency and reproducibility of the proposed techniques. These questions should be carefully studied for accurate and ethical application of this methodology in casework. Inspired by a real investigation involving ink dating, the present paper discusses this particular issue throughout four main topics: aging processes, dating methods, validation procedures and data interpretation. This work presents a wide picture of the ink dating field, warns about potential shortcomings and also proposes some solutions to avoid reporting errors in court.

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Gel ink pens have become a common writing instrument in the United States. Questioned document examiners often attempt to optically differentiate gel inks from each other and from other non-ballpoint ink writings (e.g., those from roller-ball pens). Since early formulations were primarily pigment-based, they do not elute when analyzed by thin-layer chromatography. However, recent gel ink formulations (i.e., within the past five years) include dye-based inks that can be easily separated. This study differentiates black gel inks using optical and chemical techniques. The techniques include: microscopy, visible and near infrared reflectance, near infrared luminescence, thin-layer chromatography (TLC), spot tests, and gas chromatography/mass spectrometry (GC/MS). As a result of this study a flow chart has been developed allowing for a systematic determination of a questioned ink. In addition, an analysis of volatile compounds found in gel inks revealed that there are some unique ingredients that may be found in gel inks that are not typically found in other non-ballpoint inks.