Type I Error Inflation of the Separate-Variances Welch t test with Very Small Sample Sizes when Assumptions Are Met

This Monte Carlo study shows that the separate-variances Welch t test has inflated Type I error rates at very small sample sizes, especially when sample sizes are very small in one group and larger in the second group – even when all assumptions for the statistical test are met

Solvent-Induced Shifts in Electronic Spectra of Uracil

Highly accurate excitation spectra are predicted for the low-lying n−π* and π−π* states of uracil for both the gas phase and in water employing the complete active space self-consistent field (CASSCF) and multiconfigurational quasidegenerate perturbation theory (MCQDPT) methods. Implementation of the effective fragment potential (EFP) solvent method with CASSCF and MCQDPT enables the prediction of highly accurate solvated spectra, along with a direct interpretation of solvent shifts in terms of intermolecular interactions between solvent and solute. Solvent shifts of the n−π* and π−π* excited states arise mainly from a change in the electrostatic interaction between solvent and solute upon photoexcitation. Polarization (induction) interactions contribute about 0.1 eV to the solvent-shifted excitation. The blue shift of the n−π* state is found to be 0.43 eV and the red shift of the π−π* state is found to be −0.26 eV. Furthermore, the spectra show that in solution the π−π* state is 0.4 eV lower in energy than the n−π* state

Solvent-Induced Frequency Shifts: Configuration Interaction Singles Combined with the Effective Fragment Potential Method

The simplest variational method for treating electronic excited states, configuration interaction with single excitations (CIS), has been interfaced with the effective fragment potential (EFP) method to provide an effective and computationally efficient approach for studying the qualitative effects of solvents on the electronic spectra of molecules. Three different approaches for interfacing a non-self-consistent field (SCF) excited-state quantum mechanics (QM) method and the EFP method are discussed. The most sophisticated and complex approach (termed fully self consistent) calculates the excited-state electron density with fully self-consistent accounting for the polarization (induction) energy of effective fragments. The simplest approach (method 1) includes a strategy that indirectly adds the EFP perturbation to the CIS wave function and energy via modified Hartree−Fock molecular orbitals, so that there is no direct EFP interaction with the excited-state density. An intermediate approach (method 2) accomplishes the latter in a noniterative perturbative manner. Theoretical descriptions of the three approaches are presented, and test results of solvent-induced shifts using methods 1 and 2 are compared with fully ab initio values. These comparisons illustrate that, at least for the test cases examined here, modification of the ground-state Hartree−Fock orbitals is the largest and most important factor in the calculated solvent-induced shifts. Method 1 is then employed to study the aqueous solvation of coumarin 151 and compared with experimental measurements

Interfacing the Ab Initio Multiple Spawning Method with Electronic Structure Methods in GAMESS: Photodecay of trans-Azomethane

This work presents a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane, using the ab initio multiple spawning (AIMS) program that has been interfaced with the General Atomic and Molecular Electronic Structure System (GAMESS) quantum chemistry package for on-the-fly electronic structure evaluation. The interface strategy is discussed, and the capabilities of the combined programs are demonstrated with a nonadiabatic molecular dynamics study of the nonradiative decay of photoexcited trans-azomethane. Energies, gradients, and nonadiabatic coupling matrix elements were obtained with the state-averaged complete active space self-consistent field method, as implemented in GAMESS. The influence of initial vibrational excitation on the outcome of the photoinduced isomerization is explored. Increased vibrational excitation in the CNNC torsional mode shortens the excited state lifetime. Depending on the degree of vibrational excitation, the excited state lifetime varies from ∼60–200 fs. These short lifetimes are in agreement with time-resolved photoionization mass spectroscopy experiments

Modeling Solvent Effects on Electronic Excited States

The effects of solvents on electronic spectra can be treated efficiently by combining an accurate quantum mechanical (QM) method for the solute with an efficient and accurate method for the solvent molecules. One of the most sophisticated approaches for treating solvent effects is the effective fragment potential (EFP) method. The EFP method has been interfaced with several QM methods, including configuration interaction, time-dependent density functional theory, multiconfigurational methods, and equations-of-motion coupled cluster methods. These combined QM–EFP methods provide a range of efficient and accurate methods for studying the impact of solvents on electronic excited states. An energy decomposition analysis in terms of physically meaningful components is presented in order to analyze these solvent effects. Several factors that must be considered when one investigates solvent effects on electronic spectra are discussed, and several examples are presented

An X-ray measurement of Titan's atmospheric extent from its transit of the Crab Nebula

Saturn's largest satellite, Titan, transited the Crab Nebula on 5 January 2003. We observed this astronomical event with the {\it Chandra} X-ray Observatory. An ``occultation shadow'' has clearly been detected and is found to be larger than the diameter of Titan's solid surface. The difference gives a thickness for Titan's atmosphere of 880 $\pm$ 60 km. This is the first measurement of Titan's atmospheric extent at X-ray wavelengths. The value measured is consistent with or slightly larger than those estimated from earlier Voyager observations at other wavelengths. We discuss the possibility of temporal variations in the thickness of Titan's atmosphere.Comment: 14 pages, 5 figures, AASTeX preprint. Accepted for publication in the Astrophysical Journa