Methanol Z matrix

Calculation using a z matrix (internal coordinates) in nwchem, with a little bit of help from openbabel: Assuming that you set up a calculation in e.g. ECCE for a geometry optimisation of methanol you'll end up with the following input file Last update Mai, 23 rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung/DataPrivacyStatement rd 2018 by A. Gelessus, Impressum, Datenschutzerklärung. Because the Z-matrix is not widely known among mathematicians, we will give a (Gaussian style) Z-matrix for the molecule methanol CH3OH (see Figures 2 and 3): j =0 j=1 Lj=2 µj=3 ' i=1 C i=2 OC1:5 i=3 H1 C 1:0 O 109:5 i =4 H2 C 1:0 O 109:5 H1 120 i =5 H3 C 1:0 O 109:5 H1 ¡120 i =6 HO1:0C109:5 H1 60 The column and row labels are not part of. At the high level of accuracy with which we are concerned, the {ab initio} calculation results are sensitive to the Z-matrix chosen. 2. All our results on structural and fundamental vibrational frequency changes preserve the plane of symmetry for methanol (symmetry operation: $\gamma \rightarrow \gamma \pm \pi)$, whereas not all the results.

For the mathematical meaning of this term see Z-matrix (mathematics). In chemistry, the Z-matrix is a way to represent a system built of atoms. A Z-matrix is also known as an internal coordinate representation The following is an input file for the optimization of methanol with the AMBER force field: #P amber opt=Z-Matrix geom=connectivity AMBER opt methanol, explicit connectivity 0 1 H-H1- C-CT- 1 r2 O-OH- 2 r3 1 a3 H-HO- 3 r4 2 a4 1 180.0 H-H1- 2 r5 3 a5 1 d5 H-H1- 2 r5 3 a5 1 -d5 r2=1.08105957 r3=1.39956997 r4=0.94629421 r5=1.08744287 a3=107. Methanol is a much less symmetric system whose most stable conformation is of C s symmetry. This property can be represented in the following Z-Matrix: #P HF/6-31G(d) freq HF/6-31G(d) freq methanol staggered 0 1 H1 C2 1 r2 O3 2 r3 1 a3 H4 3 r4 2 a4 1 180.0 H5 2 r5 3 a5 1 d5 H6 2 r5 3 a5 1 -d5 r2=1.08105957 r3=1.39956997 r4=0.94629421 r5=1. The most-used Z-matrix format uses the following syntax: Element-label, atom 1, bond-length, atom 2, bond-angle, atom 3, dihedral-angle [ format-code] Although these examples use commas to separate items within a line, any valid separator may be used

methanol ชื่ออื่น hydroxymethane methyl alcohol methyl hydrate wood alcohol carbinol เลขทะเบียน เลขทะเบียน CAS [67-56-1] RTECS number: PC1400000 SMILE For methanol, the primitive coordinates are defined by means of a z-matrix. It is important to note that all the hydrogen atoms of the methyl fragment are defined identically: for a hydrogen H i (see Fig. 1 ), we define the H i C distance ( r i ), the H i CO valence angle ( θ i ) and the H i COH dihedral angle ( ϕ i )

The z-matrix editor allows complete control over the z-matrix which will be submitted to the computational engine. This flexibility is particularly helpful when setting up partial geometry optimizations (in which some molecular coordinates are held fixed) and coordinate scans In this study, the relative pK a values of nine anilinium derivatives in methanol (MeOH), acetonitrile (AN), and tetrahydrofurane (THF) solutions were successfully calculated with mean absolute deviations of 0.63, 0.68, and 0.75 pK a units, respectively. To this aim, their gas‐phase basicities were computed using the CBS‐QB3 composite method. Also, conductor‐like polarizable continuum. Getting started: Geometry optimization of ethanol. This tutorial will help you to: create a simple molecule. view the molecule from all sides and save a picture. make a couple of changes to the molecule with different tools. set up your ADF calculation. perform the actual ADF calculation

Optimized coordinates (Z-matrix) for tautomers Page S7-S10 Optimized coordinates for mechanism investigations Page S11-S62 The ground state is stabilized more efficiently due to the additional hydrogen bond of methanol (above) with nitrogen lone pair. Other methanol molecule was the same (have similar interaction) for both GS and TS For methanol, a Z -matrix was created using the interatomic distances and angles found in solid α -methanol, and FOX was instructed to treat the molecule as a rigid body Because the methanol is recycled, only carbon monoxide, hydrogen, and oxygen are consumed. One plant with a production capacity of 200 000 tons of ethylene glycol per year is in Inner Mongolia, and a second plant in the Chinese province of Henan with a capacity of 250 000 tons per year was scheduled for 2012. As of 2015, four plants in China with a capacity of 200 000 t/a each were operating. To determine the Z-matrix you might want to sketch each molecule on a piece of paper and determine the bonds, angles and dihedrals you need to describe the system. You may assume that the CH 3 group has a tetrahedral conformation with a C-H bond length of 1.1Å. The C-O bond length can be estimated at 1.4Å, the O-H bond with 0.95Å


512. Briefly: zmatrices in nwchem -- methano

Find 2-AMINO-1-(3,4-DIHYDROXYPHENYL)ETHAN-1-ONE and related products for scientific research at MilliporeSigm The program call first creates a coord file from the given input structure and sorts the z-matrix (ZSORT). Then the length of the MTD simulation is determined and the algorithm is started. The following output can be expected (some printout was discarded for the documentation): 3COH] conformers in methanol Naphthalene is a white, volatile, solid polycyclic hydrocarbon with a strong mothball odor. Naphthalene is obtained from either coal tar or petroleum distillation and is primarily used to manufacture phthalic anhydride, but is also used in moth repellents.Exposure to naphthalene is associated with hemolytic anemia, damage to the liver and neurological system, cataracts and retinal hemorrhage E Herbst, JK Messer, FC DeLucia A new Analysis and Additional Measurements of the millimeter and Submillimeter Spectrum of Methanol J. Mol. Spect. 108, 42-57, 1984 10.1016/0022-2852(84)90285-6 1998Gus/Rui:16

Construction of Z-Matrix - Jacobs Universit

  1. e. These were imported using their chemical names in Avogadro. Input files were created through the Gaussian extension with. #p B3LYP/6-31G(d) scf=tight formcheck. and z-matrix (compact) [2, 3]. GaussView was used to run the programs. Cubegen generated the density and potential cubes [4]
  2. The methanol cation is the only isomer produced when methanol is used as a precursor. When ethylene glycol is used as the precursor, methylene-oxonium is produced in addition to the methanol cation
  3. Biphenyl is a benzenoid aromatic compound that consists of two benzene rings connected by a single covalent bond. Biphenyl occurs naturally in coal tar, crude oil, and natural gas. Formerly used as a fungicide for citrus crops

Electric dipole moments calculated from atom charges compared to dipoles from the wavefunction. The electric dipole moment is a measure of the charge distribution in a molecule. The calculated dipole moments are reported as an unsigned total dipole and as three cartesians components in units of Debye. to change dipole units ii WUN LIB. s f 3 7 & SiS/ APPROVAL of a thesis submitted by Ann Marie Bowler This thesis has been read by each member of the thesis committee and has been found to be satisfactory regardin View Module 1 Lab 1 and Handouts.pdf from CHEM 126 at University of California, Los Angeles. Lab 1, Module 1. Chem-126/226. 35 points. We will learn about the several standard ab initio electroni MATRIX beim führenden Marktplatz für Gebrauchtmaschinen kaufen. Jetzt eine riesige Auswahl an Gebrauchtmaschinen von zertifizierten Händlern entdecke A solution of FeCl 2 (0.197 g, 1.55 mmol) in methanol (1 ml) was added to the cooled with a single freely floating metal ion and an idealized half bdp 2− ligand defined using z-matrix.

  1. Editing the Z-matrix for your model Optional job control issues Interactive vs. background or NQS run mode Selecting a machine and base directory Setting up NQS-mode jobs Choosing the executable and setting memory limits Lesson 1: Energetics of Methanol in Water Compared with Gas Phase Lesson 2: Exploring the CH4 + Cl -> CH3 + HCl reaction.
  2. Fixing an angle in a z-matrix is straight forward. You need to specify that you are doing a partial optimisation (popt) and move the fixed parameter to the constants section. As an example, I am fixing the COH angle, and also invoke symmetry. The methanol example is as follows
  3. To perform a frozen PES scan, set FROZEN_SCAN to be TRUE and use input geometry in Z-matrix format. The example demonstrates a frozen PES of the C1-C2 bond stretching from 1.0 Åto 2.0 Åfor methanol. Example 10.219 One-dimensional frozen PES scan of methanol
  4. Infrared cavity ringdown spectroscopy of methanol clusters: Single donor hydrogen bonding. The Journal of Chemical Physics, 1999. Gregory Tschumper. Richard Saykally. Robert Provencal. Katja Roth. Henry Schaefer
  5. COSMO: Conductor like Screening Model¶. You can study chemistry in solution, as contrasted to the gas phase, with the implementation in ADF of the Conductor like Screening Model (COSMO) of solvation .The energy derivatives can also be calculated, so geometry optimization, harmonic frequencies, et cetera are available within this model
  6. 8.16 gateway. The Gateway module collects information about molecular system (geometry, basis sets, symmetry) to be used for future calculations. Gateway module is a subset of seward.All keywords for this module can also appear as an input for SEWARD, however, for clearity the information about molecular system can be placed as an input for this module

In case of the molecule having internal degrees of freedom that should be explicitly optimized, the molecule path must point to a z-Matrix and the first line in the definition is the flexy keyword <MOLECULE> flexy MoleculePath=methanol.zmat </MOLECULE> It should be noted that the zmat-format chosen is of for was described in Z-matrix notation to reduce the degrees of freedom. During the SA runs, an overall atom site occupancy factorwasvaried along with the position and torsion angles of 1-propanethiol. After the annealing converged to a global minimum, the overall atom site occupancy factor was found to be 0.9, indicating that as much as 10% of the. Methanol has been selected as the simplest representative of the homologous series of monohydric alcohols. The results show that the formation of the TF configuration corresponds to the most negative interaction energy value in the vacuum, as well as in all solvents. simulations with an additional genetic z-matrix crossing (GC) approach for. 9.2 Constrained Optimization 9.2.1 Introduction. Constrained optimization refers to the optimization of molecular structures (transition or equilibrium) in which certain parameters (e.g., bond lengths, bond angles or dihedral angles) are fixed.Jon Baker's Optimize package implemented in the Q-Chem program has been modified to handle constraints directly in delocalized internal coordinates. The solution was concentrated and the residual oil was dissolved with methanol (˜15 mL) before concentration, which was repeated 4 times. The resulting residue was dissolved in methanol, and stirred in ice bath before addition of triethylamine (1.5 mL, 10.76 mmol) followed by di-tert-butyl dicarbonate (593 mg, 2.72 mmol)

How Does the Structure of Methanol Change When the Methyl

Thermochemical parameters of three C2H5O• radicals derived from ethanol were reevaluated using coupled-cluster theory CCSD(T) calculations, with the aug-cc-pVnZ (n = D, T, Q) basis sets, that allow the CC energies to be extrapolated at the CBS limit. Theoretical results obtained for methanol and two CH3O• radicals were found to agree within ±0.5 kcal/mol with the experiment values. A set. The three dummy atoms DM1,DM2,DM3 are necessary to allow for instance a z-matrix entry for atoms C01, C05 and H06. ProtoMS is executed by calling the binary file protoms3 with a command file as input. You should inspect the command file: Parameter files: Set the path to input files containing force field parameters surfaces in methanol. Mahesh B. Dawadi and David S. Perry. a) Department of Chemistry, The University of Akron, Akron, Ohio 44325-3601, USA (Received 5 March 2014; accepted 31 March 2014; published online 22 April 2014) A set of seven conical intersections (CI's) in methanol between vibrationally adiabatic surfaces is reported

S2 Experimental Details Syntheses of 2a-4: Microcrystalline powder of 2a was prepared by mixing a methanol solution (8 mL) of ZnBr2 (0.24 mmol) into a nitrobenzene/methanol solution (32 mL/ 4 mL) of 1 (0.16 mmol). Within 30 seconds white powder was precipitated, then isolated in 48% yield by filtration. The single crystals of 2b were grown from a double-layered solution consisting of a methanol The mechanism of the disproportionation of 2,5-diethyl-3,4-dihydro-2H-pyran-2-carbaldehyde in the Cannizzaro reaction in ethanol was studied by quantum-chemical modeling. The geometry was optimized by the semiempirical RM1 method in the unrestricted Hartree-Fock approximation, and the heats of formation of the reagents and transitional states were calculated. Two possible hydride transfer. NIOSH/OSHA. Up to 1300 ppm: (APF = 25) Any supplied-air respirator operated in a continuous-flow mode £. (APF = 25) Any powered, air-purifying respirator with organic vapor cartridge (s) £. (APF = 50) Any chemical cartridge respirator with a full facepiece and organic vapor cartridge (s BC (BC), as the most common malignancy in women worldwide, is associated with high morbidity and mortality. However, chemoresistance and toxicity are the main causes that limit the success of treatment in aggressive BC cases. Thus, there is a vital need to identify and develop novel therapeutic agents. Frankincense, pine needle and geranium essential oils have been reported to play critical.

Ethylene glycol is a useful industrial compound found in many consumer products, including automotive antifreeze, hydraulic brake fluids, some stamp pad inks, ballpoint pens, solvents, paints, plastics, films, and cosmetics; it also is used as a pharmaceutical vehicle Here are a number of sample Gaussian input files. All geometries have been optimized at the RHF/3-21G level of theory

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Force Field Calculations in Gaussia

vibrational frequencies - LM

The bucket holder was thermostatically kept at 37 °C. Autofluorescence of the cellular lysate was less than 6% at any time. The fluorescent signals of both methanol (vehicle) and the substrates were recorded at the baseline, before DCF formation. DCF was quantified from a standard curve (Sigma Aldrich, St. Louis, MO, USA) in methanol Toxoplasma and Plasmodium are the parasitic agents of toxoplasmosis and malaria, respectively, and use perforin-like proteins (PLPs) to invade host organisms and complete their life cycles. The Toxoplasma gondii PLP1 ( Tg PLP1) is required for efficient exit from parasitophorous vacuoles in which proliferation occurs. We report structures of the membrane attack complex/perforin (MACPF) and. A solution of Mn (NO 3) 2 (1.0 g, 5.6 mmol) in methanol (10 mL) was prepared in a Schlenk tube. A layer of methanol (10 mL) was added on top of the solution by slow addition with a syringe. A third layer was formed by the slow addition of a solution of ethylenediamine (1.1 mL, 16.5 mmol) in methanol (10 mL) 1. Nausea and Headache. According to the US National Institutes of Health Toxicology Data Network, large doses (800 mg to 1500 mg) of theobromine may cause side effects such as nausea, headache, sweating and headache ( 29, 30 ). A daily intake to this magnitude is similar to approximately 50 g to 100 grams of cocoa

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  1. The injection volume was 1 µl, and the quadrupole mass analyzer was operated using an electrospray ionization source in the negative mode with selective ion monitoring of 491.0 m/z. Matrix and solvent calibration standards ranged from 0 to 1,035 ppb (g/vol.) in methanol
  2. utes in the dark and permeabilized in ice-cold 90% methanol for 30
  3. Finally, gels were stained with Coomassie blue R-250 (0.05% Comassie blue R-250, 30% methanol, and 10% acetic acid) for 3 hours and destained with destaining solution (20% methanol, 10% acetic acid, and 70% double-distilled H 2 O). Nonstaining bands representing the levels of the latent forms of MMP-9 were captured by a CCD camera
  4. The modulation of bone ECM is regulated by several types of matrix metalloproteinase (MMP); however, MMP-2 activity in different trabecular bones in response to resistance training (RT) has been neglected. Remodeling differs in different bones under the application of the same mechanical loading. Thus, we investigated the effects of 12 weeks of.
  5. An incomplete solvent exchange by methanol results in a shrinking of the pores during activation induced by hydrogen bonding between remaining coordinating Rietveld method using TOPAS. 48 In the course of refinement the linker molecules were treated as rigid bodies using the Z-matrix notation allowing the translation and the rotation of the.
  6. Dichloromethane/methanol (v/v = 2:1) was then added to each of the three vials to make the total volume of 200 μL. This resulted in three sample groups with spiked-in compound standards. The concentration of compound stand- value is used to search the entire m/z matrix to extract all ion
  7. g bond to 2.2 Å (iii) opt=(ts,calcfc,noeigentest,internal) If this fails (i) do set of constrained optimizations at R=1.8 to 3.0 Å on 0.2 Å grid (ii) Find maximum in Eopt (R) (iii) Use geometry from maximum in Eopt (R) as starting geometry fo

Constructing Z-Matrices Gaussian

  1. Test0521: Methanol mp2 PCM optimization and frequency: #p rmp2/6-31g* 5d freq=numer polar scrf=check test geom=allcheck: Test0522: Methanol cation mp2 PCM optimization and frequency: #p ump2/6-31g* 5d freq=numer polar scrf=check test geom=allcheck: Test0523: 2-layer ONIOM optimization and frequencies, numerical and analyti
  2. This output is from an Opt Freq calculation on methanol. Following that are essentially 0, the lowest modes (ignoring sign) are located at around 14, 19 and 25 wavenumbers. If we rerun the calculation using tight optimization criteria and a larger integration grid (Opt=Tight Int=UltraFine), the lowest modes become
  3. and digested with 0.1% trypsin for 20
  4. <Z-matrix: For examples, see: ref-data> <Blank line> OLDGEO THERMO(298,298,0) <Blank line> <Blank line> Entropies for Individual Species used in Preparing this Graph (All values are in cal/(degree.mole)
  5. The following is an input file for the optimization of methanol with the AMBER force field: Prompted by the geom=connectivity keyword the program reads after the end of the Z-Matrix definition additional lines (one per atom) that define the bonds present in the system. The line: 1 2 1.

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(Hypercube, 2010) for both - R and S enentiomer. The molecules were described in terms of Fenske-Hall Z-matrix format ans structure solutions The dihedral angles C21—C22—O7—C25; N11—C8—C20—C15 and C2—C6—C14—N4 were defined as intramolecular degrees of freedom and were varied during the structure determinations. S1.1 Recursive Z-matrix Did Jesus imply that demons are fallen spirits sided with Satan in Luke 10:17-20? Connecting 6 dots with 6 curves more hot questions Question feed Subscribe to RSS Question feed To subscribe to this RSS feed, copy and paste this URL into your RSS reader.. exchange with methanol; pores are filled with methanol, two water molecules coordinating to Cu1) and after activation under vacuum at various temperatures or for different periods. The remaining water molecules were treated as rigid bodies using the Z-matrix notation allowing translation of th Next, 3-amino-1,2-propanediol (232 μL, 3 mmol) was added to the solution, and the resulting reaction mixture was stirred overnight at room temperature. The solvent was removed in vacuo, and the resulting residue was purified by flash column chromatography on silica gel (DCM/methanol = 10/1, v/v) to yield 1 as a black solid (249 mg, 82%)

Quantum dynamics with sparse grids: A combination of

  1. The first mixture contains 40wt% methanol and the second contains 70wt% methanol. If 200g of the first mixture is combined with 150g of the second, what are the mass and composition of the product? Homework Equations The Attempt at a Solution the first solution .4*200=80 the second .7*150=105 80+105=350x x=52.9%wt methanol amount is 150+200=350
  2. Constant for the Reaction of Methanol with Atomic Hydrogen, J. Phys. Chem. A 1999 103, 4893. SM5.43 Thompson, J. D.; Cramer, C. J.; Truhlar, D. G New Universal Solvation Model and Comparison of the Accuracy of the SM5.42R, SM5.43R, C-PCM, D-PCM, and IEF-PCM Continuum Solvation Models for Aqueous and Organic Solvation Fre
  3. The WWII German Me-163 rocket plane was powered by high pressure steam created by mixing highly concentrated Hydrogen Peroxide with a mixture of methanol and water. The fuel and reaction itself was insanely dangerous, but if you're looking for a rocket powered interceptor, this might be the way to go
  4. PRSS3/mesotrypsin is an atypical isoform of trypsin that has been associated with breast, lung, and pancreatic cancer cell malignancy. In analyses of open source transcriptional microarray data, we find that PRSS3 expression is upregulated in metastatic prostate cancer tissue, and that expression of PRSS3 in primary prostate tumors is prognostic of systemic progression following prostatectomy

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Acetone Safety Data Sheet according to Federal Register / Vol. 77, No. 58 / Monday, March 26, 2012 / Rules and Regulations Date of issue: 11/12/1998 Revision date: 04/24/2018 Supersedes: 04/24/2018 Version: 1. On the physical interpretation of ab initio normal-mode coordinates for the three C-H stretching vibrations of methanol along the internal-rotation path. Journal of Molecular Spectroscopy, 2013. Li-hong Xu. Ronald Lees. Li-hong Xu. Ronald Lees. Download PDF. Download Full PDF Package. This paper The retinoblastoma (Rb)-E2F transcriptional regulatory pathway plays a major role in cell-cycle regulation, but its role in invasion and metastasis is less well understood. We find that many genes involved in the invasion of cancer cells, such as matrix metalloproteinases (MMP), have potential E2F-binding sites in their promoters. E2F-binding sites were predicted on all 23 human MMP gene. Idiopathic pulmonary fibrosis is a devastating lung disorder of unknown etiology. Although its pathogenesis is unclear, considerable evidence supports an important role of aberrantly activated alveolar epithelial cells (AECs), which produce a large variety of mediators, including several matrix metalloproteases (MMPs), which participate in fibroblast activation and lung remodeling. MMP-1 has.

To understand MMP function in mammary epithelial cells, we have focused on stromelysin-1 (SL-1), because of its diverse molecular targets (Lochter and Bissell, 1997).In the normal mammary gland, SL-1 is synthesized by fibroblasts but not by epithelial cells (Witty et al., 1995).Although SL-1 is produced at all stages of postnatal mammary gland development, its expression is highest during. ADAMTS expression can be associated with several inflammatory processes, and has been correlated with tumorigenesis of some neoplasms, but its participation in the development of periapical lesions has not been investigated. Therefore, our objective was to verify the expression of ADAMTS-1, versican and pEGFR in Periapical Granuloma (PG) and in the Radicular Cyst (RC) since they are the most. Ionizing radiation (IR) in combination with microtubule stabilizing agents (MSA) is a promising combined treatment modality. Supra-additive treatment responses might result from direct tumor cell killing and cooperative indirect, tumor cell-mediated effects on the tumor microenvironment. Here we investigated deregulation of matrix metalloproteinase (MMP) activity, as an important component of.

Relative pKa of some anilinium derivatives in methanol

Getting started: Geometry optimization of ethanol


The crystal structure of methanol monohydrate (CD3OD · D2O

The hepatocyte growth factor (HGF) is required for the activation of muscle progenitor cells called satellite cells (SC), plays a role in the migration of proliferating SC (myoblasts), and is present as a soluble factor during muscle regeneration, along with extracellular matrix (ECM) molecules. In this study, we aimed at determining whether HGF is able to interact with ECM proteins. Full Article. Research on the suitability of organosolv semi-chemical triticale fibers as reinforcement for recycled HDPE composites. Nour-Eddine El Mansouri, a Francesc X. Espinach, b, * Fernando Julian, b Narcís Verdaguer, b Lluís Torres, c Miquel F. Llop, a and Pere Mutje a The main objective of this research was to study the feasibility of incorporating organosolv semi-chemical triticale. Despite intensive chemotherapy and surgery treatment, lung and bone metastasis develop in about 30% of patients with osteosarcoma. Mechanisms for this preferential metastatic behavior are largely unknown. We investigated the role of the chemokine receptor 4 (CXCR4)/stromal cell-derived factor 1 (SDF-1) system to drive the homing of osteosarcoma cells

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Role of matrix metalloproteinase-9 in transforming growth factor-beta1-induced epithelial-mesenchymal transition in esophageal squamous cell carcinoma Xue Bai,1 Yun-yun Li,1,2 Hong-yan Zhang,1 Feng Wang,1 Hong-liu He,1 Jin-chao Yao,1 Ling Liu,1 Shan-shan Li1 1Department of Pathology, Basic Medical College of Zhengzhou University, 2Department of Stomatology, The First Affiliated Hospital of. Recent Progress in Materials(ISSN 2689-5846) Journal Flyer. Recent Progress in Materials is an international peer-reviewed Open Access journal published quarterly online by LIDSEN Publishing Inc. This periodical is devoted to publishing high-quality papers that describe the most significant and cutting-edge research in all areas of Materials

Ethane Molecule Image | Pre-Designed Illustrator GraphicsMolecular Electrostatic Potential Maps (MEPs) of SomeWhat does CConnectionGLOG::ParseGLOG(), Gaussian Error meanPPT - Kinetic Energy Operator in curvilinear coordinates